Grade 7 Unit 5 - Moving Straight Ahead ExamView Question Bank
SHORT ANSWER
1. a. Which of the following tables represent linear relationships?
Table 1
Time (s) Distance (m)
0
5
1
10
2
12
3
16
4
20
Table 2
Distance (km) Money ($)
0
0
1
10
2
20
3
30
4
40
Days
0
1
2
3
4
Table 3
Money ($)
10
8
6
2
4
b. Write an equation for one of the tables that represents a linear relationship.
c. Which table(s), if any, represents a proportional relationship? Explain.
ANS:
a. Tables 2 and 3 represent linear relationships.
b. For Table 2: y = 10x
For Table 3: y = 10 – 2x
c. Table 2; the graph goes through (0,0) and the ratio of distance to amount of money for
each ordered pair is the same.
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Check Up 1
OBJ: Investigation 1: Walking Rates
NAT: CC 7.EE.B.3 | CC 7.EE.B.4 | CC 7.EE.B.4a | CC 7.RP.A.2 | CC 7.RP.A.2b | CC 7.RP.A.2c |
NAEP A1a | NAEP A1b
TOP: Problem 1.2 Linear Relationships
KEY: rates | linear relationship
2. Each graph below represents a linear relationship between time and distance.
For each graph, describe what is the rate of change?
ANS:
a. 5 meters per second; as x increases by 1 second, y increases by 5 meters.
b. 20 kilometers per hour; as x increases by 1 hour, y increases by 20 kilometers.
c. 10 miles per hour; as x increases by 1 hour, y increases by 10 miles.
PTS: 1
DIF: L2
OBJ: Investigation 1: Walking Rates
REF: Moving Straight Ahead | Check Up 1
NAT: CC 7.EE.B.3 | CC 7.EE.B.4 | CC 7.EE.B.4a | CC 7.RP.A.2 | CC 7.RP.A.2b | CC 7.RP.A.2c |
NAEP A1a | NAEP A1b
TOP: Problem 1.3 Using Linear Relationships
KEY: rates | linear relationship
3. a. Jason is participating in a walkathon. He writes the equation
to represent the amount
of money he collects from each sponsor for walking d kilometers. What number represents the rate
of change?
b. Cierra is keeping track of the amount of money in her lunch account each week. She writes the
equation
. What number represents the rate of change?
ANS:
a. The coefficient of d is the rate of change, so Jason collects $2 per kilometer.
b. The equation can be written as
, so the rate of change is –6 dollars per week.
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Check Up 1
OBJ: Investigation 1: Walking Rates
NAT: CC 7.EE.B.3 | CC 7.EE.B.4 | CC 7.EE.B.4a | CC 7.RP.A.2 | CC 7.RP.A.2b | CC 7.RP.A.2c |
NAEP A1a | NAEP A1b
4. Mark opens a bank account with $20. Each week he plans to put in $5.
a. Make a table to show the total amount of money Mark has in his bank account. Show the
amount he has in his account from 0 to 10 weeks.
b. Make a graph that matches the table.
c. Write an equation to represent the total money Mark has in his account over time.
d. In which week will Mark have a total of $60. Explain your reasoning.
ANS:
a.
Week
0
1
Money
in
Account
$20
$25
2
3
4
5
6
7
8
9
10
$30
$35
$40
$45
$50
$55
$60
$65
$70
b.
c.
d. Week 8; If you use the table, you can look to see where $60 appears in the Money in Account
column, which is Week 8. If you use the graph, find 60 on the y-axis and see where that intersects
with the line, then follow it down to see which week goes with that value. If you use the equation,
substitute $60 in for y (which represents the total amount of money in the account) and solve the
equation for x (which represents the week).
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Check Up 1
OBJ: Investigation 1: Walking Rates
NAT: CC 7.EE.B.3 | CC 7.EE.B.4 | CC 7.EE.B.4a | CC 7.RP.A.2 | CC 7.RP.A.2b | CC 7.RP.A.2c |
NAEP A1a | NAEP A1b
5. Find the value of the indicated variable.
a. Suppose y = 2x + 10. Find y if x = –2.
b. Suppose y = 2x – 2.5. Find x if y = 10.
ANS:
a. y = 6; Students may make a table for this equation or may substitute the value for x in the equation.
b. x = 6.25; Students may make a table for this equation or may substitute the value for y in the
equation and solve for x.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Check Up 2
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs
solving equations | tables and graphs
6. Solve each equation to find the value of x.
a. 4x + 10 = 22
b. 3x + 9 = 6x
c. 2(x + 3) = 18
d. 2x + 15 = 27 – 4x
ANS:
a. x = 3
b. x = 3
c. x = 6
d. x = 2
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Check Up 2
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
7. LaShawn wants to buy some music online. There are two plans to choose from. The first plan is a flat
rate of $1.29 per download. The second plan has a membership fee of $21, and a fee of $0.99 per
download. Let x be the number of downloads and C be the cost.
Plan 1:
Plan 2:
a. When are the costs of the two plans equal to each other? Explain.
b. What is the y-intercept of the line for each equation? What does it mean in this context?
c. What is the constant rate of change for each relationship? What does it mean in this context?
d. For Plan 1, how many downloads are possible if the total cost is at most $15? Explain.
ANS:
a. When LaShawn purchases 70 songs, the cost will be the same for both plans.
b. Plan 1: The y-intercept is 0, which means there is no upfront costs and if you buy 0 songs, you
pay $0. Plan 2: The y-intercept is 21, which means there is an upfront cost of $21 before you buy
any songs.
c. Plan 1: The constant rate of change: is $1.29 per song, the coefficient of x. Plan 2: The constant
range of change: is $.99 per song.
d. 11 downloads at most means less than or equal to, so you can write the inequality
for
Plan 1. If you substitute 15 for C, you get
. Since the solution is
, and the
number of songs must be a whole number, you can download at most 11 songs.
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Check Up 2
OBJ: Investigation 3: Solving Equations
NAT: CC 7 EE.A.2 | CC 7.EE.A.1 | CC 7.EE.B.3 | CC 7.EE.B.4 | CC 7.EE.B.4a | CC 7.EE.B.4b
8. The graph of the money Jake earns while babysitting is shown below.
a. Put a scale on each axis that makes sense for this situation. Explain why you chose the scales
you did.
b. Based on the scale you chose in part (a), what would the equation of the graph be?
c. If the line on this graph were steeper, what would it tell you about the money Jake is making?
Write an equation for such a line.
ANS:
Answers will vary. Sample answers are given for a rate of $4 per hour.
a.
b. Sample answer: y = 4x.
c.
If the line were steeper, it would mean that Jake’s rate of dollars per hour would be greater.
Answers for the equation may vary, Possible answer: y = 6x.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Partner Quiz
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.4 Connecting Tables, Graphs, and Equations
linear function | tables and graphs
9. Rachael’s backyard swimming pool is being emptied by a pump. The amount of water in the pool (W,
measured in gallons) at any time (t, measured in hours) is given by the following equation:
a. How many gallons of water are being pumped out each hour? Explain how you got your
answer.
b. After 11 hours, how much water is left in the pool? Explain.
c. How much water was in the pool at the start? Explain.
d. How long will it take the pool to empty? Explain.
ANS:
a. 250 gallons are being pumped out of Rachel’s pool per hour. The coefficient of t is –250, so as 1
hour passes, W decreases by 250. Students could also make a table of values or a graph and see the
same rate of change.
b. After 11 hours, there are 9000 – 250(11) = 6250 gallons left in the pool. Students may use a
table, a graph, or numeric reasoning.
c. When t = 0, W = 9,000, so 9,000 gallons were in the pool at the start.
d. It takes 36 hours to empty the pool. Students should first find the value of t when W = 0. They can
use a table, a graph, or an equation. If they use an equation, they should set W = 0 and solve for t:
9,000 – 250t = 0
t = 36
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Partner Quiz
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
10. Jabal and Michael are walking to school and agree to leave their homes at the same time. Jabal leaves
his house walking 2 meters per second. Michael leaves his house walking at 2.5 meters per second.
Jabal’s house is 100 meters closer to school than Michael’s house. After how long are the boys
walking together? Show all your work.
ANS:
It takes 200 seconds, or 3 minutes and 20 seconds, for Michael to catch up to Jabal. One way to solve
this problem is to write an equation for each person’s distance from Michael’s house. When the two
distances are equal, Jabal and Michael will meet.
Jabal’s distance from Michael’s house is given by y = 2x + 100.
Michael’s distance from his own house is given by y = 2.5x.
So we solve for x in the following equation:
2.5x = 2x + 100
0.5x = 100
x = 200 seconds, or 3 minutes 20 seconds
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: Moving Straight Ahead | Partner Quiz
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.1 Finding the Point of Intersection
KEY: linear function
11. Use the graph at the right.
a. Find the slope of the line.
b. Find the equation of the line.
ANS:
a. The slope is 3. Encourage students to check several points on the line. For example, the slope
using (0, 2) and (1, 1) is 3, as is the slope between (1, 1) and (2, 4).
b. y = 3x – 2
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: Moving Straight Ahead | Unit Test
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 KEY: slope | equations with two variables
12. Does the table below represent a linear relationship? If so, write an equation for that relationship. If
not, explain.
Time (s)
0
3
7
9
10
ANS:
Yes. The equation is
PTS:
OBJ:
NAT:
TOP:
Distance
(m)
11
17
25
29
31
.
1
DIF: L2
REF: Moving Straight Ahead | Unit Test
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.B.3 | CC 7.EE.B.4 | CC 7.EE.B.4a | CC 7.RP.A.2b | CC 7.RP.A.2c | CC 7.RP.A.2d
Problem 1.2
13. Solve each equation for x. Show your work.
a. 3x + 8 = 35
b. 12 + 5x = 7x + 3
c. 3(x + 1) = 12
ANS:
a. x = 9
b. x = 4.5
c. x = 3
PTS: 1
DIF: L2
OBJ: Investigation 3: Solving Equations
REF: Moving Straight Ahead | Unit Test
NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
TOP: Problem 3.4 KEY: solving equations | linear equations
14. Multiple Choice
Which of the following expressions is not equivalent to the others? Explain.
A.
B.
C.
D.
ANS:
C; When simplified, the other three expressions are equivalent to
the expression is
.
PTS:
OBJ:
NAT:
TOP:
. When choice C is simplified,
1
DIF: L2
REF: Moving Straight Ahead | Unit Test
Investigation 3: Solving Equations
CC 7 EE.A.2 | CC 7.EE.A.1 | CC 7.EE.B.3 | CC 7.EE.B.4 | CC 7.EE.B.4a | CC 7.EE.B.4b
Problem 3.4
15. Match a table (A–D) with a graph (E–H) and an equation (I–L). List your results below in four
groups. For example, on the line for group 1 you should put 3 letters, one for a table, one for a graph
and one for an equation which all represent the same linear pattern.
Group 1:
Table: _______
Graph: _______
Equation: _____
A.
Group 2:
Table: _______
Graph: _______
Equation: _____
B.
Group 3:
Table: _______
Graph: _______
Equation: _____
C.
Group 4:
Table: _______
Graph: _______
Equation: _____
D.
x
y
x
y
x
y
x
y
–2
–5
–2
3
–2
1.5
–2
–3
–1
–3
–1
2
–1
1.5
–1
–1
0
–1
0
1
0
1.5
0
1
1
1
1
0
1
1.5
1
3
2
3
2
–1
2
1.5
2
5
J.
K.
L.
M.
ANS:
Note: Since students are asked to form four groups, the naming of each group is arbitrary. Sample
answer:
Group 1: A, F, K
Group 2: B, H, M
Group 3: C, G, J
Group 4: D, E, L
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: Moving Straight Ahead | Unit Test
Investigation 4: Exploring Slope
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 4.2 KEY: rates | linear relationship
16. To encourage customers, a new movie theater is offering different ways to pay for a movie.
• Members: $75 a year plus $2 per movie.
• Nonmembers: $5.75 to see a movie.
a. Make one table that shows the number of movies n and the cost for members C1. Make another
table that shows the number of movies n and the cost for nonmembers C2. For both tables,
include values of n from 0 to 50 movies, in increments of 10.
b. On the same set of axes, graph the relationship of cost and number of movies for members and
for nonmembers.
c. Write equations that you can use to calculate the cost for members C1 and non-members C2,
for any number of movies n.
Equation for members: _________________________
Equation for nonmembers: ______________________
d.
What is the sllope of each line in part (c)?
Slope of equation for members: _________________________
Slope of equation for nonmembers: ______________________
e. What information does the slope of each line represent about the member and nonmember
costs?
f.
Explain how you could find slope from a table, a graph, and an equation.
g. What information does the y-intercept of each line represent about the member and
nonmember costs?
h. For what number of movies will the cost be the same for both members and nonmembers?
Explain how you found your answer.
ANS:
a.
n
n
0
75
0
0
10
95
10
57.50
20
115
20
115.00
30
135
30
172.50
40
155
40
230.00
50
175
50
287.50
b.
c.
d. The slope of the line for members is 2.
The slope of the other line for nonmembers is 5.75.
e. The slope of each line represents the constant rate of change, or the cost per movie.
f. From the table, you can compare the quantities in any two rows. The slope is the ratio of the
change in cost to the change in number of movies. From the graph, you can find the slope using
any two points on the line. The slope is the ratio of the vertical change to the horizontal change.
From the equations, the slope is the coefficient of n in each equation.
g. The y-intercept represents the cost if a person does not go to the movies at all. For a member, the
y-intercept is 75. For a nonmember, the y-intercept is 0.
h. 20 movies
75 + 2x = 5.75x
75 = 3.75 x
20 = x
PTS:
OBJ:
Slope
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Unit Test
Investigation 1: Walking Rates | Investigation 3: Solving Equations | Investigation 4: Exploring
NAT:
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 1.3 | Problem 3.5 | Problem 4.2
slope | finding the slope of a line
17. Each equation below represents a linear relationship between x and y. For each equation, describe what
happens to the y value as the x value increases by 1.
a. y = x + 50
b. y = –5x + 10
ANS:
a. For y = x + 50, as x increases by one unit, y increases by one unit.
b. For y = –5x + 10, as x increases by one unit, y decreases by 5 units.
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.3 Using Linear Relationships
KEY: rates | linear relationship
18. Does the table below represent a linear relationship? Explain how you know.
x
0
1
2
3
4
y
0
15
30
45
60
ANS:
Yes; Since as x increases by one y increases by 15. There is a constant rate of change.
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.3 Using Linear Relationships
KEY: rates | linear relationship
19. The pep club is going to sell bouquets of flowers during the homecoming game. They represent their
sales, R, and costs, C, with the following equations.
R = 5.50x
C = 250 + 1.25x x is the number of bouquets.
a. When is the pep club’s sales equal to their costs? Explain how you got your answer.
b. What is the y-intercept for the line of each equation? What does it mean in this context?
c. What is the constant rate of change for each relationship? What does it mean in this context?
ANS:
a. To find out when the revenue (income) and cost are equal, we find x so that 5.50x = 250 + 1.25x.
We can solve this by graphing or by using tables or by using a symbolic method. To solve by
graphing, draw the two linear graphs and find their point of intersection (student would have to
estimate the actual intersection point). To solve symbolically:
4.25x = 250
x 58.8, so about 59 bouquets.
When they sell 59 bouquets, the cost and revenue will both be approximately $324. Students may
also write that if they sell 58 bouquets, they will have a slight loss, and if they sell 59 bouquets,
they will make a slight profit.
b. The y-intercept for the revenue equation is (0, 0) because if the store sells no bouquets, they will
make no money. The y-intercept for the cost equation is (0, 250) because even if the store does not
sell a single bouquet, the operation will cost them $250.
c. The constant rate of change for the revenue function is 5.5. This means that for each bouquet they
sell, they will bring in $5.50. The constant rate of change for cost is 1.25, which means that each
bouquet will cost an additional $1.25 over the original start-up cost.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.5 Finding the Point of Intersection
solving equations | point of intersection
20. Brent's Video Shack charges $1.50 to rent a video game for a night. Mr. Buck's Entertainments opens a
new store in town, charging $1.00 per night for a game, and starts to take customers away from Brent's
Video Shack.
a. Graph each price scheme on the same set of axes.
b. How could Brent change his charges, so that he includes a one-time membership fee and lowers
his rental fee below Mr. Buck's, to get his customers back without losing too much money? Graph
your proposal, and explain to Brent how it will work.
ANS:
a.
b. Possible answer: Brent might charge a membership fee of $5 and then $.50 per game per night. For
the first 10 games, Brent's customers will pay more, but after 10 games their total cost will be lower
than if they rented from Mr. Buck's. Brent should advertise his plan, emphasizing that if you are a
frequent customer you will be better off at Brent's.
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.3 Comparing Equations KEY: linear function | comparing functions
21. Does it make a difference what two points you choose on a straight line to find the slope of the line?
Explain your answer.
ANS:
It does not matter which two points you use to determine the slope of a straight line. Since there is a
constant rate of change between any two points on a straight line, the slope is the same between any
two points on that line.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
slope | finding the slope of a line
22. Big A's Bike Rentals charges $300 plus $20 per bike to rent bikes for a week. Little Cheeper's rental
shop charges $50 plus $35 per bike for a week. You need to determine which company to use for your
bike-touring project. Write an explanation to a student who has never used a graphing calculator to
help that student display and solve this problem on a graphing calculator.
ANS:
On the appropriate screen you need to enter the equations Y1 = 300 + 20X and Y2 = 50 + 35X, where
X represents the number of bikes. Next you need to set a window appropriate for the context, maybe x
values from 0 to 20 and y values corresponding to these, say from 0 to 700. When you graph these
equations, you will see two lines giving the costs for the two companies. The point where the lines
cross is the point where the two plans cost the same for that number of bikes. Before or after that point,
one company or the other has the better deal.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.5 Finding the Point of Intersection
solving equations | point of intersection
23. Gretchen was absent when the class developed strategies for solving linear equations. Write an
explanation to her about how to solve equations using the symbolic method. Use the equation
4n – 17 = 43 as an example.
ANS:
You can think of solving an equation like this one as reversing the procedure that was done to create
the expression on the left. To make 4n – 17 you would multiply n by 4 and then subtract 17. To reverse
this, you add 17, then divide by 4.
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.3 Writing Equations
KEY: solving equations | writing equations
24. a. This table shows two points that are on the same straight line. Complete the table to show three
other points on the same line.
b. Find the slope and the y-intercept of this line that represents the data.
ANS:
a.
x
y
b. slope
PTS:
OBJ:
NAT:
TOP:
KEY:
-3
-2
-2
0
-1
2
0
4
1
6
, y-intercept
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
slope | finding the slope of a line
25. Given one of the representations below, find the other two.
Table
Graph
Equation
y=
x+1
y=
x+1
a. Find the y-intercept for each representation above.
b. Find the slope for each representation above.
ANS:
Table
Graph
Equation
y = –3x + 8
y = 4x – 3
a. The y-intercepts are 8, –3, and 1.
b. The slopes are –3, 4, and
PTS:
OBJ:
NAT:
TOP:
KEY:
.
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
slope | finding the slope of a line
26. Sam made up a set of tables based on some equations. He gave the tables to Adrian and challenged her
to find the equations for each table. Adrian added two columns to each table to help her find the
equations. Adrian used the extra columns to find the differences in x values and y values for each table.
Below is the start of her work.
a. Adrian used the extra columns to find the differences in x values and y values. Complete these
columns for each table.
b. Describe any patterns you see in the columns of differences.
c. Find the equation of any table that represents a linear relationship.
d. Explain why Adrian added the columns to the tables Sam gave her. Do you think it helped her
to find the equations? Explain your thinking.
ANS:
a.
b. In tables A and D, both x and y increase by constant amounts. The ratios of these amounts,
change in y : change in x, is always constant (2 : 1 for Table A and D). In table B, x-values
increase by increments of 2, but y-values increase and then decrease making first positive changes
then negative changes. The ratio change in y : change in x, is not constant. In table C, neither x
nor y increases by constant amounts. However, change in y : change in x is always 1: 2.
c. Table A: y = 2x + 3
Table C: y =
x+1
Table D: y = 2x – 1
d. Adrian added the columns to help her look at how the increments in the y values changed in
relation to how the increments in the x values changed. In linear relationships, these changes will
both be constant. Once Adrian had determined which of the tables represented linear relationships,
she could find the related equations, because the ratio of the increments is the slope of the line.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.4 Connecting Tables, Graphs, and Equations
linear function | tables and graphs
27. The formula relating n (the number of cricket chirps per minute) to t (the temperature in degrees
Fahrenheit) is
.
a. Using a symbolic method, find how many times a cricket would chirp in a minute at 90 F.
b. It is evening, and a cricket is chirping 48 times per minute. Use a symbolic method to find the
temperature.
ANS:
a.
b.
chirps per minute
The temperature is 52F.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
Refer to this table, which Francine, Geraldo, and Jennifer made during a bicycling trip. It shows the
distance each person traveled during the first four hours of their trip. The table shows the distance
covered while the students were actually biking. (Time is not counted when they stop to rest, eat, etc.)
Distance (miles)
Cycling Time (hours)
0
1
2
3
4
Francine
0
4.5
9
13.5
18
Geraldo
0
6
12
18
24
Jennifer
0
7.5
15
22.5
30
28. a. How fast did each person travel for the first four hours? Explain how you arrived at your answer.
b. Assume that each person continued at this rate. Find the distance each person traveled in 6 hours.
ANS:
a. Francine: 4.5 mph; Geraldo: 6 mph; Jennifer: 7.5 mph; Divide the number of miles traveled in 4
hours by 4.
b. Francine: 27 miles; Geraldo: 36 miles; Jennifer: 45 miles
PTS:
REF:
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TOP:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.1 Finding and Using Rates
KEY: rates
29. a. Graph the time and distance for all three people on the same coordinate axes.
b. Use the graphs to find the distance each person traveled in 2.5 hours.
c. Use the graphs to find the time it took each person to travel 70 miles.
d. How does the rate at which each person rides affect the graphs?
ANS:
a.
b. Students' estimates should be close to the following values: Francine: 11.25 miles; Geraldo: 15
miles; Jennifer: 18.75 miles
c. Students' estimates should be close to the following values: Francine: 15.6 hours; Geraldo: 11.7
hours; Jennifer: 9.3 hours
d. The faster the cyclist, the steeper the graph.
PTS:
REF:
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1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.1 Finding and Using Rates
KEY: rates
30. a. For each rider, write an equation you can use to calculate the distance traveled after a given
number of hours.
b. Describe how you could use your equations to calculate the distance each person traveled in 2.5
hours.
c. How does each person's biking rate show up in the equation?
ANS:
a. Francine: D = 4.5t; Geraldo: D = 6t; Jennifer: D = 7.5t
b. Substitute 2.5 for t in each equation.
c. the number being multiplied by t
PTS:
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DIF: L2
Moving Straight Ahead | Additional Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.2 Linear Relationships KEY: rates | linear relationship
31. a. Stilton was also on the bike trip. The distance he traveled after t hours is represented by d = 7.25t.
At what rate of speed was he traveling?
b. If you were to put the graph of Stilton's distance and time on the same set of axes as the graphs for
Francine, Geraldo, and Jennifer, how would it compare to the other three graphs?
ANS:
a. 7.25 miles per hour
b. Stilton's graph would be steeper than Francine's and Geraldo's but less steep than Jennifer's.
PTS:
REF:
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NAT:
TOP:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.3 Using Linear Relationships
KEY: rates | linear relationship
32. Each set of (x, y) coordinates below is generated by a linear rule. For each set of coordinates, write an
equation to describe the rule.
a. (–1, –7), (0, -3), (1, 1), (2, 5), (4, 13), (5, 17)
b. (–2, 19), (–1, 14), (0, 9), (2, –1), (4, –11), (6, –21)
c. (–2, –1), (0, 3), (1, 5), (3, 9), (5, 13), (6, 15)
ANS:
a. y = 4x – 3
PTS:
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b. y = 9 – 5x
c. y = 2x + 3
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.2 Linear Relationships KEY: rates | linear relationship
Use the graph below to answer the questions.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
Line A
–4
–5
Line B
33. a. Make a table showing the coordinates of four points located on line A. What is the equation for
line A?
b. Make a table showing the coordinates of four points located on line B. What is the equation for
line B?
c. Is there a point with (x, y) coordinates that satisfy both the equation for line A and the equation for
line B? Explain your reasoning.
ANS:
a. y = x + 3
x
0
y
3
–1
2
–2
1
–3
0
b. y = 1 - x
x
0
y
1
1
0
2
–1
3
–2
c. Yes, the point is (–1, 2), which is where the two lines intersect on the graph. The point (–1, 2) is on
both lines so it satisfies both equations.
PTS:
REF:
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1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.3 Using Linear Relationships
KEY: rates | linear relationship
34. Martin used some rules to generate the following tables:
a
On grid paper, make a graph of the data in each table. Show the graphs on the same coordinate
axes.
b. Which sets of data represent a linear relationship? How do you know?
ANS:
a.
b. Sets i, ii, and iii represent linear relationships, The graphs of these data sets are straight lines.
PTS:
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1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.4 Recognizing Linear Relationships
KEY: rates | linear relationship
Do parts (a) – (e) for each equation.
a. Graph the equation on your calculator, and make a sketch of the line you see.
b. What ranges of x and y values did you use for your window?
c. Do the y values increase, decrease, or stay the same as the x values increase?
d. Give the y-intercept.
e. List the coordinates of three points on the line.
35. i.
y = 2.5x
ANS:
a.
ii. y = –2x + 7
iii. y = –4x - 8
iv. y = 3x – 3
b.
c. i. increase
ii. decrease
iii. decrease
d. i. 0
ii. 7
iii. -8
iv. increase
iv. -3
e. i.-iv. Answers will vary.
PTS:
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KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.4 Connecting Tables, Graphs, and Equations
linear function | tables and graphs
36. The volleyball team decided to raise money for an end-of-season party by selling school buttons. The
costs and the revenue of selling the buttons are shown on the graph below.
a. If the team sells 50 buttons, what will be their cost? What will be the revenue?
b. If the team sells 50 buttons, how much profit will they make? (Remember that the profit is the
revenue minus the cost.)
c. If the team sells 100 buttons, how much profit will they make?
ANS:
a. $25; $50
b. $25
c. $100 - $50 = $50
PTS:
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1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.3 Comparing Equations KEY: linear function | comparing functions
37. a. Graph the equation y = 5x + 7 on your calculator. Use the graph to find the missing coordinates for
these points on the graph: (2, ?), (?, 52), and (2.9, ?).
b. Graph the equation y = 1.5x – 4 on your calculator. Use the graph to find the missing coordinates
for these points on the graph: (10, ?) and (?, 32).
c. Graph the equation y = 6.25 – 3x on your calculator. Use the graph to find the missing coordinates
for these points on the graph: (5, ?) and (–2.75, ?).
ANS:
a. (2, 17), (9, 52), (2.9, 21.5)
b. (10, 11), (24, 32)
c. (5, -8.75), (–2.75, 14.5)
PTS:
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KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.4 Connecting Tables, Graphs, and Equations
linear function | tables and graphs
38. Use the graph below to answer (a)-(d).
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
a. List the coordinates of three points on the line.
b. Which equation below is the equation of the line?
i.
y=x+4
ii. y = 0.5x + 2
iii. y = 0.5x - 5
iv. y = 4 - 0.5x
c. Does the point (56, 35) lie on the line? Explain your reasoning.
d. Does the point (–20, –8) lie on the line? Explain your reasoning.
ANS:
a. Possible answer: (-4, 0), (0, 2), and (2, 3)
b. ii. y = 0.5x + 2
c. no; The x value 56 corresponds to the y value 30, not 35.
d. yes; The x value –20 does correspond to the y value –8.
PTS:
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KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.4 Connecting Tables, Graphs,| and Equations
linear function | tables and graphs
39. Here is a graph of three lines.
a. Complete the chart.
line
A
B
C
constant rate of change
y-intercept
x-intercept
b. Here are the equations of the three lines. Match each line with its equation.
,
,
line A: ____________,
line B: ____________,
line C: ____________
ANS:
The equation for the line labeled A: y = 3 – x; the equation for the line labeled B: y = 2 + x; the
equation for the line labeled C: y = – 4 + 2x
a.
line
A
B
C
constant rate of change
–1
1
2
b. line A: y = 3 – x,
PTS: 1
line B: y = 2 + x,
DIF: L2
y-intercept
(0, 3)
(0, 2)
(0, –4)
line C: y = –4 + 2x
x-intercept
(3, 0)
(–2, 0)
(2, 0)
REF:
OBJ:
NAT:
TOP:
Moving Straight Ahead | Additional Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.3 Comparing Equations KEY: linear function | comparing functions
40. Here is a graph of two lines:
a. What is alike about these lines? What is different?
b. The equation for line A is
make the equation for line B?
. What do you think would have to change in order to
c. Write the equation for line B.
d. Imagine a line halfway between lines A and B. What do you think its equation is? Explain
your thinking.
ANS:
The equation of the line labeled A: y = x + 3; The equation of the line labeled B: y = x + 1
a.
b.
c.
d.
PTS:
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TOP:
They are parallel; they cross the y-axis at different points
Change the constant value of 3 to 1
y=x+1
y = x + 2; 2 is halfway between 3 and 1
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.3 Comparing Equations KEY: linear function | comparing functions
41. Here is a graph of a line:
a. Complete this table.
x
–3
y
0
2
5
7
10
100
b. Explain your thinking for the last three rows.
ANS:
The graph is of the equation
a.
x
–3
0
2
5
7
10
100
y
–2
–1
0
1
2
4
49
b. For each increase in x, the value of y increases by
90, there is a change of
PTS:
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TOP:
KEY:
. So from 10 to 100, which is a change of
times 90 or 45.
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.4 Connecting Tables, Graphs, and Equations
linear function | tables and graphs
42. a. For each pair of lines, find the point of intersection.
and
and
and
and
b. What pattern do you see?
c. Without graphing the lines, where is the point of intersection of these lines?
and
ANS:
a. y = x
y=x+1
y=x+3
and
and
and
y = -x
y = –x + 1
y = –x + 3
(0, 0)
(0, 1)
(0, 3)
y=x-4
and
y = –x – 4
(0, -4)
b. The y-coordinate of the point of intersection is the common constant term in the two equations
c. (0, 137)
PTS:
REF:
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1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.1 Finding the Point of Intersection
KEY: linear function
43. The equations below represent the costs to print brochures at three different printers.
a. For which equation does the point (20, 60) lie on the graph? Explain.
i.
C = $15 + $2.50N
ii. C = $50 + $1.75N
iii. C = $30 + $1.50N
b. For each equation, give the coordinates of a point on the graph of the equation.
ANS:
a. Equation iii because the point satisfies the equation: 60 = 30 + 1.5(20).
b. Answers will vary.
PTS:
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KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs
solving equations | tables and graphs
44. The equations below represent the distances in meters traveled after t seconds by three cyclists.
a. For which equation does the point (10, 74) lie on the graph? Explain.
i.
D = 2.4t + 32
ii. D = 4.2t + 32
iii. D = 6t + 32
b. For each equation, give the coordinates of a point on the graph of the equation.
ANS:
a. Equation ii because the point satisfies the equation: 74 = 4.2(10) + 32.
b. Answers will vary.
PTS:
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KEY:
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DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs
solving equations | tables and graphs
45. Do parts (a)-(c) for each pair of equations below.
i.
y=–
x–6
ii. y = x – 3
iii. y = x + 9
iv. y = 2x – 6
y = 4x + 14
y = –1.5x + 12
y = 7 – 3x
y = –2
a. On your calculator, graph the two equations on the same axes. Use window settings that allow you
to see the point where the graphs intersect. What ranges of x and y values did you use for your
window?
b. Find the point of intersection of the graphs.
c. Test the point of intersection you found by substituting its coordinates into the equations. Did the
point fit the equations exactly? Explain why or why not.
ANS:
a.
b. The exact answers are given here. If students found the intersection points by inspecting the
graphs, their answers may not be exact.
i. (–3.125, 1.5)
ii. (6, 3)
iii. (–0.5, 8.5) iv. (2, –2)
c. The values may not fit exactly because they may be estimates, but they should be close.
PTS:
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1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
TOP: Problem 3.5 Finding the Point of Intersection
KEY: solving equations | point of intersection
46. a. Find r if 2r + 10 = 22.
c. Find z if 3z – 19 = 173.
ANS:
a. r = 6
c. z = 64
PTS:
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KEY:
b. Find x if 4.5x = 45.
d. Find w if 67.1 = 29.7 – 0.2w .
b. x = 10
d. w = –187
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
47. Betty is thinking of two consecutive integers whose sum is 41. Let x represent the smaller unknown
integer.
a. How could you represent the larger unknown integer in terms of x?
b. Write an equation showing that the sum of the two unknown integers is 41.
c. Solve your equation. What integers is Betty thinking of?
ANS:
a. x + 1
b. x + (x + 1) = 41
c. The equation in (b) is the same as 2x + 1 = 41. Subtracting 1 from both sides gives us 2x = 40, so
x = 20 and x + 1 = 21.
PTS:
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Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
48. Find the number described in each problem by writing and solving an equation.
a. If Sarah subtracts five times her number from 24, she gets 4. What is Sarah's number?
b. Twice Bill's number added to 17 is 7. What is Bill's number?
c. The sum of 4 times a number and 14 is 16. What is the number?
d. If Susan subtracts 11 from one-fourth of her number she gets 11. What is Susan's number?
ANS:
a. 24 – 5x = 4; 4
b. 2x + 17 = 7; x = –5
c. 4x + 14 = 16; x =
d.
x – 11 = 11; x = 88
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Additional Practice Investigation 3
OBJ:
NAT:
TOP:
KEY:
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
49. The school drama club is performing its summer play at the community theater. Props for the play cost
$250, and the theater is charging the drama club $1.25 for each ticket sold. So, the total cost C, for the
drama club to put on the play is C = 1.25N + 250, where N is the number of tickets sold. Customers
pay $4 for each ticket, so the total amount collected from ticket sales is T = 4N.
a. What is the cost if 213 tickets are sold?
b. How much is the total ticket sales if 213 tickets are sold?
c. What is the drama club's profit or loss if 213 tickets are sold?
d. If the total ticket sales are $780, how many people attended the play?
e. What is the cost of putting on the play for the number of people you found in part (d)?
f.
How many tickets does the drama club need to sell to break even?
g. The drama club would like to earn a profit of $500 from the play. How many tickets need to be
sold for the club to meet this goal?
ANS:
a. $516.25
b. $852
c. $335.75 profit
d. 195
e. $493.75
f. 91
g. 273
PTS:
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DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.5 Finding the Point of Intersection
solving equations | point of intersection
50. In each pair, solve the first equation and graph the second equation:
a.
b.
c.
d. In each pair, how is the solution related to the graph?
ANS:
a. x = -2; graph with x-intercept (-2, 0)
b. x = 2; graph with x-intercept (2, 0)
c.
; graph with x-intercept (
, 0)
d. the solution is the x-coordinate of the x-intercept
PTS: 1
DIF: L2
REF:
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Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs
solving equations | tables and graphs
51. Marsha said there are two ways to solve the equation
subtract 15 from each side
divide each side by 3
divide each side by 3
subtract 5 from each side
a. Are both strategies correct? Explain.
b. Which strategy do you think is easier? Explain.
c. How do you know when you can divide first?
d. Solve this equation in two ways:
ANS:
a. Both are correct
b. Answers will vary
c. Dividing is reasonable if all the values are divisible by the same number
d. 5x = –15
x+4=1
x = –3
x = –3
PTS:
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KEY:
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DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
52. Find x if
a.
b.
c.
d. How are the solutions similar? How are they different?
ANS:
a. x = 13
b. 3x = 13 so x =
c. –2x = 13 so x =
d. The numerators of the solutions are all 13; the denominators are the coefficients of x
PTS:
REF:
OBJ:
NAT:
TOP:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
KEY: solving equations | linear equations
53. If
, find y if
a.
b.
c.
d.
e.
f.
ANS:
a. y = 4
b. y = 6
c. y = 10
d. y = -2
e. y = 10
f.
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
y=4
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
54. Solve the following equations for the value of x:
a. 3x + 5 = 4x – 10
b. 4x + 10 = 6x – 8
d. 3x – 11 = 8x – 21
e. 3(x + 8) = 12
ANS:
a. x = 15
d. x = 2
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
b. x = 9
e. x = –4
c. 3x + 10 = 5x
c. x = 5
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
55. Find the slope and y-intercept of the line represented by each equation.
a. y = 2x – 10
b. y = 4x + 3
d. y = 2.6x
e. y = 7x + 1
c. y = 4x – 4.5
ANS:
a. slope is 2; y-intercept is –10
b. slope is 4; y-intercept is 3
c. slope is 4; y-intercept is –4.5
d. slope is 2.6; y-intercept is 0
e. slope is 7; y-intercept is 1
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Additional Practice Investigation 4
OBJ: Investigation 4: Exploring Slope
NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
TOP: Problem 4.2 Finding the Slope of a Line
KEY: slope | finding the slope of a line
56. Each table in i-v below represents a linear relationship. Do parts (a)-(c) for each table.
a. Find the slope of the line that represents the relationship.
b. Find the y-intercept for the graph of the relationship.
c. Determine which of the following equations represents the relationship.
y = 3 – 4x, y = x + 6, y = 4x – 3, y = 3x – 1.5, y = 2.5x
ANS:
i. a. 2.5
b. 0
c. y = 2.5x
ii. a. 1
b. 6
c. y = x + 6
iv. a. –4
b. 3
c. y = 3 – 4x
v. a. 4
b. –3
c. y = 4x – 3
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
iii.
a. 3
b. –1.5
c. y = 3x – 1.5
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
slope | finding the slope of a line
57. For each of the lines below, find the slope, and write an equation that represents the line.
ANS:
a. slope is 1; y = x
b. slope is – ; y = – x
c. slope is –3; y = –3x
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
58. Do parts a-d for each pair of points below.
i.
(0, 0) and (–3, -3)
ii. (1, –1) and (–3, 3)
a. Plot the points on a coordinate grid, and draw the line through the points.
b. Find the slope of the line through the points.
c. Estimate the y-intercept from the graph.
d. Using your answers from parts (a) and (b), write an equation for the line through the points.
ANS:
a.
b. i. slope = 1
c. i. y-intercept = 0
d. i. y = x
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
ii. slope = –1
ii. y-intercept = 0
ii. y = –x
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
59. On Saturdays, Jim likes to go to the mall to play video games or pinball. Round-trip bus fare to and
from the mall is $1.80. Jim spends $0.50 for each video or pinball game.
a. Write an equation for the amount of money, M, it costs Jim to go to the mall and play n video
or pinball games. Explain your reasoning.
b. What is the slope of the line your equation represents? What does the slope tell you about this
situation?
c. What is the y-intercept of the line? What does the y-intercept tell you about the situation?
d. How much will it cost Jim to travel to the mall and play 8 video or pinball games?
e. If Jim has $6.75, how many video or pinball games can he play at the mall?
ANS:
a. M = 0.5n + 1.80
b. 0.5 is slope; It is the cost of each game.
c. 1.80 is the y-intercept; It is the bus fare.
d. $5.80
e. Jim can play 9 games, and he will have $0.45 left over.
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
60. Angie likes to take the bus to the Comic Shop downtown. Below is a graph showing the total cost
(including bus fare and the cost of comics) for her to go to the Comic Shop to buy new comic books.
a. What is Angie's round-trip bus fare? Explain your reasoning.
b. How much does a comic book cost at the Comic Shop? Explain your reasoning.
c. Write an equation that shows how much money, M, it costs Angie to buy n comic books at the
Comic Shop. What information did you use from the graph to write the equation?
ANS:
a. $2.25; This is the intercept on the y-axis, which represents the cost if Angie buys 0 comics.
b. $1.50; For each comic book purchased, the cost rises by $1.50.
c. Using the slope and the y-intercept, the equation is M = 1.5n + 2.25.
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
61. Tonya is siphoning all the water from a full aquarium to clean it. The graph below shows the amount
of water left in the aquarium as Tonya siphons the water.
a. How much water was in the aquarium when it was full? Explain your reasoning.
b. How much water does the siphon remove from the aquarium in 1 minute? Explain your
reasoning.
c. Write an equation that shows the amount of water, G, left in the aquarium after t minutes.
d. How many gallons of water are left in the aquarium after 10 minutes?
e. How long will it take the siphon to remove all of the water from the aquarium? Explain your
reasoning.
ANS:
a. 45 gallons; This is the y-intercept (the amount of water in the aquarium at t = 0).
b. From the graph, the siphon removes 20 gallons in 12 minutes, or equivalently,
=
gallons
in 1 minute.
c. G =
t + 45
d. Substitute 10 for t in the equation. You get G = 28.33 gallons of water left in the aquarium.
e. Substitute 0 for G in the equation. You get t = 27 minutes.
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
62. In (a) – (f), write an equation for the line that satisfies the given conditions.
a. The slope is 7 and the y-intercept is -2.
b. The slope is 0 and the y-intercept is 9.18.
c. The line passes through the points (3, 1) and (6, 4).
d. The line passes through the points (–24, –11) and (–8, –3).
e. The line passes through the points (–4.5, 2) and (6.3, 5.8).
f.
The slope is
and the line passes through the point (5, 0).
ANS:
a. y = 7x – 2
b. y = 9.18
c. y = x – 2
d. y = 0.5x + 1
e. y =
f.
x+
y=
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
63. Write an equation for each of the four lines shown on the graph below.
ANS:
The equations for the lines are:
L1:
L2:
L3:
L4:
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
64. At Midtown Bowling Center, the cost to bowl four games is $8.40, and the cost to rent shoes is $1.15.
a. Write an equation for the cost, C, for renting shoes and bowling n games.
b. What is the y-intercept for your equation, and what does it represent?
c. What is the slope of your equation, and what does the slope represent?
d. What is the cost of renting shoes and bowling six games?
e. Tony paid $7.45 for his games and shoe rental. How many games did Tony bowl?
ANS:
a. C = 2.1n + 1.15
b. 1.15; This is the cost for shoe rental.
c. 2.1; This is the cost of bowling each game.
d. $13.75
e. Tony bowled 3 games.
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
65. Here are some possible descriptions of a line:
A. positive slope
B. slope equals 0
C. negative slope
D. positive y-intercept
E. y-intercept equals 0
F. negative y-intercept
G. passes through the origin: (0, 0)
H. crosses the x-axis to the right of the origin
K. crosses the x-axis to the left of the origin
L. never crosses the x-axis
For each equation below, list ALL of the properties that describe the graph of that equation.
a.
b.
c.
d.
ANS:
a. A, E, G
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
e.
b. A, D, K
c. B, F, L
d. C, D, H
e. C, F, K
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
66. a. These two points determine a line: (0, 3) and (2, 5). Which of the following points are also on that
line?
(4, 7)
(4, 8)
(4, 10)
b. These two points determine a line: (–2, 10) and (1, 4). Which of the following points are also on
that line?
(2, 0)
(2, 2)
(2, 10)
ANS:
a. (4, 7); Since the equation of the line is: y = x + 3
b. (2, 2); since the equation of the line is: y = 6 – 2x
PTS:
REF:
OBJ:
NAT:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
TOP: Problem 4.4 Writing Equations with Two Variables
KEY: slope | equations with two variables
67. Below are four patterns:
“1 square”
“2 square”
“3 square”
“4 square
a. In each cell in the chart below, write the PERIMETER of the figure:
shape
1 square
2 squares
3 squares
4 squares
1 copy
2 copies
3 copies
4 copies
10 copies
100 copies
b. What changes as you add more copies to each pattern?
c. Explain how you found the values for the last three columns.
d. Write an equation for the PERIMETER of figures for each shape.
ANS:
a.
shape
1 square
2 squares
3 squares
4 squares
1 copy
4
6
8
10
2 copies
6
8
10
12
3 copies
8
10
12
14
4 copies
10
12
14
16
10 copies
22
24
26
28
100 copies
202
204
206
208
b. The perimeter increases by 2.
c. For the 4 copies you can just look at a picture and find the perimeter or you can see the pattern is
increasing by two. For ten copies you know that between 4 and 10 there are 6 columns so it would
increase by 2 six times so there is an increase of 2 6 to the 4 copies column which makes 22 for
the 10 copies column. For 100 copies you can do the same thing with this row and the 10 copies
row and find out that the ten copies row increased by 2 90 = 180.
d. 1 square: P = 2N + 2, where N = number of copies
2 square: P = 2N + 4, where N = number of copies
3 square: P = 2N + 6, where N = number of copies
4 square: P = 2N + 8, where N = number of copies
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
68. Line A is the graph of this equation:
Line B is the graph of this equation:
a. What is alike about these lines? What is different?
b. Write the equation of a line that lies between line A and line B. How is your equation similar to
the equations above? How is it different?
c. Explain why your equation is correct.
ANS:
a. The slopes are the same; the y-intercepts are different
b. y = 2x + K, where K is any number strictly between 2 and 0; for example,
c. The new line has the same slope so it is parallel to the original two lines; the new constant term is
between the original constant terms, so the y-intercept of the new line is between the y-intercept of
the original two lines.
PTS:
REF:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
Moving Straight Ahead | Additional Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
69. A student, who is studying walking rates, enters the rule y = 40 + 2x into the calculator and produces
this graph. He has highlighted one point on the graph.
a. What question could the student be trying to answer by using the graph?
b. Write the question for part (a) as an equation that could be used to find the answer.
ANS:
a. He might be trying to determine how long it would take before a walker was 216 meters from the
start OR how far the walker was from the start after 88 seconds.
b. To solve the problem of finding how long it would take before the walker was 216 meters from the
start, the equation would be 216 = 40 + 2x.
OR
To solve the problem of finding how far the walker was from the start after 88 seconds, the
equation would be y = 40 + 2(88).
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: Moving Straight Ahead | Question Bank
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.1 Finding and Using Rates
KEY: rates
MULTIPLE CHOICE
1. Which of the following data sets is linear?
A.
C.
B.
D.
ANS:
REF:
OBJ:
NAT:
TOP:
B
PTS: 1
DIF: L2
Moving Straight Ahead | Multiple Choice
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.4 Recognizing Linear Relationships
KEY: rates | linear relationship
2. Which of the following is linear?
A. y = 2 + 3x
ANS:
REF:
OBJ:
NAT:
TOP:
B. y = 2x(x + 5)
C. y = 4x2
D. y = 2x
A
PTS: 1
DIF: L2
Moving Straight Ahead | Multiple Choice
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.4 Recognizing Linear Relationships
KEY: rates | linear relationship
Use the following table to answer the questions.
X
Y
1
4
2
7
3
10
4
13
3. What is the slope of data set?
A. 4
B. 3
C. 1
ANS: B
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Multiple Choice
OBJ: Investigation 4: Exploring Slope
D. 9
NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
TOP: Problem 4.2 Finding the Slope of a Line
KEY: slope | finding the slope of a line
4. What is the y-intercept of the data set?
A. 4
ANS:
REF:
OBJ:
NAT:
TOP:
B. 3
C. 1
D. 13
C
PTS: 1
DIF: L2
Moving Straight Ahead | Multiple Choice
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.3 Comparing Equations KEY: linear function | comparing functions
5. What is the equation to represent the data set?
A. y = x + 3
C. y = 3x + 1
B. y = 4x + 1
D. y = 3x +13
ANS:
REF:
OBJ:
NAT:
TOP:
C
PTS: 1
DIF: L2
Moving Straight Ahead | Multiple Choice
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.3 Writing Equations
KEY: solving equations | writing equations
6. Consider the equation y = 4x – 10. Find y if x = 3.
A. 33
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
B. 12
D. –3
C. 2
C
PTS: 1
DIF: L2
Moving Straight Ahead | Multiple Choice
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
solving equations | linear equations
7. What is the equation of the line that contains the points (2, 13) and (6, 33)?
A.
y=
C.
x+3
B. y = 5x + 5
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
y=
x+5
D. y = 5x + 3
D
PTS: 1
DIF: L2
Moving Straight Ahead | Multiple Choice
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.4 Writing Equations with Two Variables
slope | equations with two variables
8. The rate of change is constant in the table. Find the rate of change. Explain what the rate of change
means for the situation.
Time (hours)
Distance (miles)
4
260
6
390
8
520
650
10
A. 10; Your car travels for 10 hours.
B. 260; Your car travels 260 miles.
C.
; Your car travels 65 miles every 1 hour.
D.
; Your car travels 65 miles every 1 hour.
ANS:
REF:
OBJ:
NAT:
TOP:
C
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.2 Linear Relationships KEY: rate of change
Find the slope of the line that passes through the pair of points.
9. (1, 7), (10, 1)
A. 3
2
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
B.

2
3
C.

3
2
D. 2
3
B
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
finding slope using points | slope
10. (–5.5, 6.1), (–2.5, 3.1)
A. –1
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
B. 1
C. –1
D. 1
A
PTS: 1
DIF: L2
Moving Straight Ahead | Skills Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
finding slope using points | slope
11. A student finds the slope of the line between (14, 1) and (18, 17). She writes
. What mistake
did she make?
A.
B.
C.
D.
She should have added the values, not subtracted them.
She used y-values where she should have used x-values.
She mixed up the x- and y-values.
She did not keep the order of the points the same in numerator and the denominator.
ANS: D
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Skills Practice Investigation 4
OBJ:
NAT:
TOP:
KEY:
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
slope | reasoning | error analysis
Write an equation in point-slope form for the line through the given point with the given slope.
12. (10, –9); m = 2
A. y – 10 = 2(x + 9)
C. y – 9 = 2(x – 10)
B. y – 9 = 2(x + 10)
D. y + 9 = 2(x – 10)
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
D
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.3 Exploring Patterns With Lines
slope-intercept form | linear equation
13. A line passes through (2, –1) and (8, 4).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
A.
B.
y+1=
5
(x – 2); –5x + 6y = –16
6
C.
y–1=
5
(x – 2); –5x + 6y = 16
6
D.
y+1=
5
(x + 2); –5x + 6y = –16
6
y–2=
5
(x + 1); –5x + 6y = 17
6
ANS: A
PTS: 1
DIF: L2
REF: Moving Straight Ahead | Skills Practice Investigation 4
OBJ: Investigation 4: Exploring Slope
NAT: CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
TOP: Problem 4.3 Exploring Patterns With Lines
KEY: point-slope form | transforming equations | standard form of a linear equation | multi-part
question
14. Is the relationship shown by the data linear? If so, model the data with an equation.
x
y
–9
–2
–5
–7
–1
–12
–17
3
A.
4
(x + 9).
5
B.
4
The relationship is linear; y + 9 =  (x + 2).
5
C. The relationship is not linear.
The relationship is linear; y + 2 =
D.
5
The relationship is linear; y + 2 =  (x + 9).
4
ANS:
REF:
OBJ:
NAT:
TOP:
D
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.4: Connecting Tables, Graphs, and Equations KEY: linear equation | linear data
Solve the equation.
15.
A. –6
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
B. 1
6
C. 216
D. 6
D
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.2 Exploring Equity
Division Property of Equality | inverse operations | algebra
16.
B. –49
A. 49
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
C. 14
D. 0
B
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.2 Exploring Equity
Multiplication Property of Equality | inverse operations | algebra
17.
A. –20
ANS:
REF:
OBJ:
NAT:
TOP:
B. –22
C. –26
D. –28
A
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.4 Solving Linear Equations
KEY: two-step equation | algebra
18.
A. –93
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
B. 7
C. –7
D. 93
C
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.2 Exploring Equity
Addition Property of Equality | inverse operations | algebra
19. The science club is selling puzzles to raise money. The supplier charges a one-time fee of $55 for each
order and $10 for each puzzle. Write and solve an equation to find the number of puzzles the science
club can buy if they have $1,245.
A. 55 + 10p = 1,245; 119 puzzles
C. 10p – 55 = 1,245; 23 puzzles
B. 65p = 1,245; 20 puzzles
D. 1,245 = 10p + 55; 130 puzzles
ANS: A
PTS: 1
DIF: L1
REF: Moving Straight Ahead | Skills Practice Investigation 1
OBJ: Investigation 1: Walking Rates
NAT: CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
TOP: Problem 1.2 Linear Relationships
KEY: write an equation | word problem | problem solving | multi-part question | algebra | two-step
equation
20. Write a unit rate for the situation. Round to the nearest hundredth if necessary.
traveling 209 km in 5 h
A. 41.8 km/h
ANS:
REF:
OBJ:
NAT:
TOP:
B. 0.02 km/h
C. 52.25 km/h
D. 34.83 km/h
A
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.1 Finding and Using rates
KEY: ratio | unit rate | rate
21. A soccer player scored 41 goals in 84 games. Express the player’s scoring rate as a unit rate rounded to
the nearest thousandth.
A. 0.4881 goals per game
C. 0.488 goals per game
B. 2.049 goals per game
D. 2.0488 goals per game
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
C
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.1 Finding and Using rates
ratio | unit rate | word problem | problem solving | decimals | rate
22. Graph the points A(5, –4 ), B(1, –2), and C(3, 3) on the same coordinate plane.
y
A.
–4
–2
y
C.
4
4
2
2
O
B
2
4
x
–4
–2
C
O
2
x
4
B
C
–2
–2
A
–4
A
–4
y
B.
D.
y
A
A
4
4
C
B
2
–4
–2
C
B
O
2
4
x
–4
–2
2
O
–2
–2
–4
–4
2
4
x
ANS: C
PTS: 1
DIF: L1
REF: Moving Straight Ahead | Skills Practice Investigation 1
OBJ: Investigation 1: Walking Rates
NAT: CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
TOP: Problem 1.2 Linear Relationships
KEY: quadrants | ordered pair | coordinates | x-axis | x-coordinate | y-axis | y-coordinate | origin |
graphing a point
Graph the linear equation.
23.
y
A.
–4
–2
y
C.
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
2
4
x
y
B.
–4
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
–2
y
D.
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
2
4
x
A
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.2 Linear Relationships
graph of an equation | linear equation | graphing a linear equation | ordered pair | algebra
1
24. y =  x
5
A.
y
–4
–2
4
4
2
2
O
2
4
x
–2
O
–2
–4
–4
y
–2
–4
–2
B.
–4
y
C.
4
2
2
2
4
x
4
x
2
4
x
y
D.
4
O
2
–4
–2
O
–2
–2
–4
–4
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
A
PTS: 1
DIF: L2
Moving Straight Ahead | Skills Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.2 Linear Relationships
graph of an equation | linear equation | graphing a linear equation | ordered pair | algebra
Find three solutions of the equation.
25.
A. (0, 0), (3, –8), (–2, 4)
B. (1, –2), (0, 0), (–1, 1)
ANS:
REF:
OBJ:
NAT:
TOP:
C. (–2, 4), (1, –2), (0, 0)
D. (–2, 4), (1, –2), (2, –3)
C
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.2 Linear Relationships KEY: ordered pair | algebra
26. y = 7x
A. (–2, –14), (3, 21), (–4, –28)
B. (0, 0), (–3, –23), (–2, –14)
ANS:
REF:
OBJ:
NAT:
TOP:
C. (3, 21), (0, 0), (–1, –6)
D. (–2, –14), (3, 21), (2, 13)
A
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 1
Investigation 1: Walking Rates
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1a | NAEP A1b
Problem 1.2 Linear Relationships KEY: ordered pair | algebra
27. Find the slope of the line.
y
6
4
2
–6
–4
–2
O
2
4
6
x
–2
–4
–6
A.

1
2
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
B. 1
2
C. 2
D. 2
B
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
slope | rise | run | slope of a line
28. Draw a line with a slope of 2 through the point (–3, –1).
y
A.
C.
–6
–4
–2
6
6
4
4
2
2
O
ANS:
REF:
OBJ:
NAT:
TOP:
2
4
6
x
–2
–4
–2
–4
–4
–6
–6
6
6
4
4
2
2
O
2
4
6
x
–6
–4
–2
O
–2
–2
–4
–4
–6
–6
4
6
x
2
4
6
x
C
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
KEY: slope | slope of a line
D. (–4, –9)
B
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs KEY: solution
30. Determine which ordered pair is NOT a solution of y =
A. (3, –9)
B. (–4, –3)
C. (–7, 0)
ANS:
REF:
OBJ:
NAT:
TOP:
2
y
D.
29. Determine which ordered pair is a solution of y =
.
A. (9, –2)
B. (–5, 18)
C. (1, –6)
ANS:
REF:
OBJ:
NAT:
TOP:
O
–2
y
–4
–6
–2
B.
–6
y
.
D. (4, –11)
A
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs KEY: solution
Graph the linear equation.
31. y =
A.
y
–4
–2
4
4
2
2
O
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
32. y =
2
4
x
–2
O
–2
–4
–4
y
–2
–4
–2
B.
–4
y
C.
4
2
2
2
4
x
4
x
2
4
x
y
D.
4
O
2
–4
–2
O
–2
–2
–4
–4
B
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs
linear equation | graph of an equation with two variables
y
A.
–4
–2
4
4
2
2
O
4
x
–2
–4
–2
O
–2
–4
–4
y
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
33. y =
2
–2
B.
–4
y
C.
4
2
2
2
4
x
4
x
2
4
x
4
x
y
D.
4
O
2
–4
–2
O
–2
–2
–4
–4
A
PTS: 1
DIF: L2
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs
linear equation | graph of an equation with two variables
2
3
y
A.
–4
–2
y
C.
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
2
y
B.
–4
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
–2
y
D.
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
2
4
x
B
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs
linear equation | graph of an equation with two variables
34. You are organizing a school banquet. You spend $82 on decorations. Dinner will cost $13 for each
person that attends. In the equation
, y is the total cost of the banquet for x people.
Complete the solution (69,
A. $991
ANS:
REF:
OBJ:
NAT:
TOP:
) to find the cost for 69 people.
B. $815
C. $979
C
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs KEY: solution
35. A slug can travel 0.3 meters per minute. In the equation
minutes. Complete the solution (43,
A. 12.9 m
ANS:
REF:
OBJ:
NAT:
TOP:
D. $965
B. 129 m
, y is the distance traveled in x
) to find how far the slug can travel in 43 minutes.
C. 143.3 m
D. 1.29 m
A
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.1 Solving Equations Using Tables and Graphs KEY: solution
Find the slope of the line.
y
36.
6
4
2
–6
–4
–2
O
2
4
6
x
–2
–4
–6
A. 2
ANS:
REF:
OBJ:
NAT:
TOP:
B.

1
2
D. 1
2
C
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 4
Investigation 4: Exploring Slope
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1f | NAEP A4d
Problem 4.2 Finding the Slope of a Line
KEY: slope | slope of a line
1
37. Identify the slope and y-intercept of y =  x
2
A. 1
B. 1
 ;7
;7
2
2
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
C. 2
.
C.
1
 ; –7
2
D. 1
; –7
2
A
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.2 Using Tables, Graphs, and Equations
y-intercept | slope-intercept form
38. Graph y =
3
x
2
using the slope and y-intercept.
y
A.
–4
–2
y
C.
6
6
4
4
2
2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
–6
–6
y
B.
2
4
x
2
4
x
y
D.
6
6
4
4
2
2
–4
–2
O
2
4
x
–4
–2
O
–2
–2
–4
–4
–6
–6
ANS:
REF:
OBJ:
NAT:
TOP:
KEY:
B
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 2
Investigation 2: Exploring Linear Functions With Graphs and Tables
CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A1b | NAEP A1c
Problem 2.2 Using Tables, Graphs, and Equations
y-intercept | slope-intercept form | slope
39. What is the solution of the following system of equations?
y = 4x
y = x
A. (4, 0)
B. (1, 3)
C. (–3, 19)
ANS:
REF:
OBJ:
NAT:
TOP:
D. (0, 7)
B
PTS: 1
DIF: L1
Moving Straight Ahead | Skills Practice Investigation 3
Investigation 3: Solving Equations
CC 7.EE.1 | CC 7.EE.3 | CC 7.EE.4 | CC 7.EE.4.a | NAEP A2b | NAEP A4c
Problem 3.5 Finding the Point of Intersection
KEY: system of linear equations