Linear Representations
A line can be represented by a graph, a table, and an equation. The three main forms that an
equation of a line can be written in are the:
Slope-Intercept Form: ___________________________
Point-Slope Form: ____________________________
Standard Form: ____________________________
Use the following graph for examples #1 - 4.
Example 1: Which of the lines is represented by
the equation y = 2x + 1?
Example 2: Which of the lines is represented by
the equation y - 1 = 2(x + 3)?
Example 3: Which of the lines is represented by
the following table?
x
-1
0
1
2
y
6
4
2
0
Example 4: Which of the lines is represented by
the equation 2x + y = -3?
Linear Functions & Tables
A linear function is a function in the form
f(x) = mx + b
where m and b are real numbers and x is a variable.
Example 1:
Example 2:
Given the equation R(t) = 300 + 100t, what are
the missing values for R(t) in the table below?
t
R(t)
2
?
Johnny is planning on going to a concert with
some of his friends. A maximum of 8 people
can fit into his car. Tickets to the concert cost
$10 each, and parking costs $40 per car. The
cost Johnny pays for attending the concert with
his friends is given by the following formula.
4
?
C = $40 + $10t
6
?
8
?
If Johnny spent $90 on the concert, how many
tickets did he buy?
Solution:
Solution:
Linear Equations from Tables
Equations from Tables
The slope intercept form of a linear equation is shown below, where m is the slope of the line and b is
the y-intercept: ___________________. The values given in a table, representing a linear function,
can be used to identify the slope and the y-intercept of the function.
The y-intercept is the point at which the line crosses _______________________________________
Slope may be found using the following formula: _________________________________________
Example:
x
y
Which of the following equations corresponds
to the table at left?
A.
y = 2x + 3
B.
y = 2x - 3
C.
y= x+3
D.
y= x-3
Question: Graph the line that passes through the points given in the following table. Write the
equation of the line in all 3 forms.
x
y
2
3
1
1
0
-1
-1
-3
Linear Functions
1. A function has y-intercept of -5 and a
slope of -3/2. Which equation at right
describes the function?
A. y = -3/2x2 - 5
B. y = -3/2x - 5
C. y = -3/2 + x - 5
D. y = -5x + -3/2
2. The monthly cost of operation at a
company, C, given in dollars as a
function of the number of units produced
per month, u, is given below.
Use the given equation to complete the
table at left.
A. 3,500; 6,500; 9,500; 12,500; 15,500;
18,500
C = 3,500 + 30u
B. 6,500; 9,500; 12,500; 15,500; 18,500;
21,500
Units Produced (u)
100
200
300
400
500
600
Monthly Cost (C)
?
?
?
?
?
?
C. 6,500; 6,530; 6,560; 6,590; 6,620; 6,650
D. 3,530; 3,560; 3,590; 3,620; 3,650; 3,680
3. Which graph corresponds to the table below?
x
y
A
B
-4
4
-3
11
-2
/3
10
C
-1
/3 3
0
8
/3
D
4. Which of the following tables
corresponds to the graph below?
A.
B.
C.
D.
x
-3
-2
-1
0
y
3
8
7
/3
2
x
-3
-2
-1
0
y
3
8
7
/3
2
x
-3
-2
-1
0
y
3
8
7
/3
3
x
-3
-2
-1
0
3
8
7
y
/3
/3
/3
/3
/3
3
1
5
/3
1
-5
/3
1
-5
/3
1
5
/3
5. The Steady Price Phone Company (SPPC) has a new calling plan that charges a flat
fee plus a per minute fee as described by the equation below. Determine which table
matches the equation.
y = $0.25x + $37.95
A.
SPPC Pricing Plan
Minutes
6
8
13
Cost
B.
C.
21
$39.45 $39.95 $42.50 $41.10
SPPC Pricing Plan
Minutes
6
8
13
Cost
21
$39.45 $39.95 $41.20 $43.20
SPPC Pricing Plan
Minutes
6
8
13
Cost
D.
$44.20 $46.20 $51.20 $59.20
SCCP Pricing Plan
Minutes
6
8
13
Cost
21
21
$39.45 $39.15 $41.20 $45.30
6. Which graph corresponds to the table below?
A
x
4
y
-1
B
5
-4
6
/3
-5
7
8
/3 -2
-7
/3
C
D
7. Benny purchased a car for $13,950. The table below shows the amount of money that
he still owes (y) after each payment (x) that he makes.
Payment (x)
1
2
3
4
Amount Owed (y)
$13,675
$13,400
$13,125
$12,850
If Benny does not change his payment amount, how much money will he still owe after
making his 8th payment?
A. $11,750
B. $12,025
C. $11,740
D. $11,475
8. Which of the following equations describes the function graphed below?
A. y = 1/2x + 3
B. y = -2x + 3
C. y = 3x + 1/2
D. y = -1/2x + 3
9. The amount of Jerry's pay every week before taxes, J, is given below as a function of
the number of overtime hours that he works (number of hours past 40), h.
J = $520.00 + $19.50·h
Overtime (h)
2
4
6
8
10
12
Weekly Pay (J)
?
?
?
?
?
?
Use the given equation to complete the table above.
A. $520.00; $539.50; $559.00; $578.50; $598.00; $617.50
B. $559.00; $578.50; $598.00; $617.50; $637.00; $656.50
C. $559.00; $598.00; $637.00; $676.00; $715.00; $754.00
D. $539.50; $559.00; $578.50; $598.00; $617.50; $637.00
10. The amount of Jerry's pay every
week before taxes, J, is given below as a
function of the number of overtime hours
that he works (number of hours past
40), h.
J = $493.60 + $18.51·h
Assuming that Jerry is only paid for each
whole hour that he works, how many
total hours would Jerry have to work
during a week to make at least $750.00?
A. 54
B. 64
C. 13
D. 53
11. Jamie is trying to lose weight. She
starts a diet and workout regimen and
records her weight (y) every week (x) at
her gym. Her initial weight was 190 lbs.
If Jamie continues to lose weight at the
same rate, how many more weeks will it
take her to reach her goal of 160 lbs?
A. 8 weeks
Week (x)
1
2
3
4
Weight (y)
187
184
181
178
B. 5 weeks
C. 6 weeks
D. 7 weeks
12.
Which of the following functions matches
the graph at left?
A.
B.
C.
D.
13. A laundromat is having a special on dry cleaning shirts. The first shirt costs $1.52.
Every shirt after the first one costs $0.62. One customer paid $15.16. Which equation
can be used to determine how many shirts the customer had cleaned?
A. $0.62x + $15.16 = $1.52
B. $1.52 - $0.62x = $15.16
C. $0.62x + $1.52 = $15.16
D. $15.16 + $1.52 = $0.62x
14. The charge to ship a package from
one town to another, C, is given below as
a function of the weight of the object, w,
in pounds.
C = $4.00 + $0.60·w
If the shipping cost for Cathy's item was
$9.58, what was it's weight?
A. 0.93 lbs
B. 9.3 lbs
C. 93 lbs
D. 19.3 lbs
15. A rancher noticed that, typically, the first day he has a new horse the horse eats 15
pounds of hay. The second day on, the horse typically eats 24 pounds of hay per day.
Which equation could be used to determine the number of pounds, y, the horse will eat
over x days?
A. y = 24(x + 15)
B. y = 24x - 15
C. y = 15x + 24
D. y = 24x + 15