Name: ________________________ Class: ___________________ Date: __________
ID: A
Linear Relations Unit Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which point would lie on the line 2x 3y
a. (-2, 1)
b. (-1, 2)
c. (1, -2)
d. (2, -1)
____
2. The graph represents a linear equation. Determine the value of y when x
7 ?
y
(0, 3)
(2, -1)
a.
b.
c.
d.
-9
-7
-5
-1.5
1
x
6.
Name: ________________________
____
3. Which equation would produce the given table of values?
a.
b.
c.
d.
____
ID: A
x
y
0
1
2
3
4
5
100
95.5
91
86.5
82
77.5
y
y
y
y
4.5x 100
4.5x 100
4.5x 100
4.5x 100
4. Which point satisfies the linear relation: 3x 2y
a. (5, 8)
b.
(5, 7)
(5, 7)
d. (5, 8)
c.
____
5. Which graph matches the equation y
2?
a.
c.
b.
d.
2
1?
Name: ________________________
____
ID: A
6. If n represents the figure number and s represents the number of sticks, which equation relates the
number of sticks to the figure number?
a.
b.
c.
d.
____
s 3n 2
n 3s 2
s 3n 5
n 3s 5
7. This pattern of unit squares continues. Which equation below relates, P (perimeter), to the figure
number, n?
Figure 1
a.
b.
c.
d.
P
P
P
P
Figure 2
Figure 3
n2
2n 4
2n 6
2n 8
3
Name: ________________________
____
ID: A
8. Which tables of values does not represent a linear relation?
a.
b.
c.
d.
____
9. Which equation describes the graph?
y
6
4
2
–6
–4
–2
0
2
4
6
–2
–4
–6
a.
b.
c.
d.
y 3x 3
y x 3
y 3x
y 3x 3
4
x
Name: ________________________
ID: A
____ 10. What is the equation of the dashed line shown on the graph?
y
4
2
-4
-2
2
-2
4
x
-4
a.
b.
c.
d.
xy 3
xy 3
x 3
y 3
Short Answer
11. Match the following equations with the appropriate graph. Justify your choice.
Equations
A: 4x y
1
B: 4x 2y
2
Graph 1
y
Graph 2
y
4
4
2
2
-4 -2
-2
2 4
x
-4 -2
-4
EQUATION:
-2
-4
EQUATION:
5
2 4
x
[2 marks]
Name: ________________________
ID: A
12. John needs to save $1800 for a trip to Europe.
A. Using the graph below, will he have saved enough money after 30 weeks? Explain
B. Did you use interpolation or extrapolation? Explain.
6
Name: ________________________
ID: A
13. Match each line with one of the equations. Show your workings to support your answer.
y 3x
1
yx
Line A: ______________
Line B: ______________
7
1
y 2x
4
Name: ________________________
ID: A
14. A local chocolate maker sells three different sizes of chocolate bars. The price of each chocolate bar
is listed below. The chocolate maker plans to make two new sizes of chocolate bars. She wants the
prices and sizes to be related to the chocolate bars she sells already.
45
55
65
50
60
Price (¢)
a) Graph the data.
70
Size (g)
1 point
Price of Chocolate Bars
140
120
Price (¢)
100
80
60
40
20
0
20
40
60
80
100
120
140
Mass (g)
b) What should the chocolate maker charge for a 100g chocolate bar?
1 point
c) What should be the size of a chocolate bar that costs $0.85?
1 point
8
ID: A
Linear Relations Unit Review
Answer Section
MULTIPLE CHOICE
1. ANS: D
&2, 1' because 2 &2' 3 &1'
4 &3'
4 &3'
7
Feedback
A
May have thought 2 &2' 3 &1'
4 3
7
B
May have thought 2 &1' 3 &2'
2 5
C
7
May have thought 2 &1' 3 &2'
25
7
D
Correct!
PTS: 1
TOP: 4.4
DIF: 2A
REF: CG p. 74,75
MSC: Linear Relations
1
OBJ: 9PR2
ID: A
2. ANS: A
Extend the line and find x 6 on the x-axis. Draw a vertical line straight down until you intersect the
extended line. Then, go across with a horizontal line until you hit the y-axis. This will intersect at 9.
Feedback
A
B
C
D
Correct!
miscounted and got 7 instead of 9
extended line incorrectly ( ruler wasn`t used)
students drew a line horizontally from 6 on the y-axis and then drew a line
vertically down to the x-axis at 1.5
PTS: 1
TOP: 4.5
DIF: 2A
REF: CG p.76
MSC: Linear Relations
2
OBJ: 9PR2
ID: A
3. ANS: B
y 4.5x 100
From the table of values you can see that there is a constant change in both the independent and
dependent variables: as x increases by 1, y decreases by 4.5. Therefore, this is a linear equation with
a numerical coefficient of -4.5.
If we replace x and y with points such as &1, 95.5' and &2, 91' we can see that a constant term of 100
is needed to preserve equality.
95.5
4.5 &1' ?
91
4.5 &2' ?
95.5
4.5 100
91
9 100
95.5
95.5
91
91
Feedback
A
Substituting &1, 95.5' would result in 95.5
95.5
B
C
4.5 100
95.5 z 104.5
Therefore this cannot be the equation.
Correct!
Substituting &1, 95.5' would result in 95.5 4.5 &1' 100
95.5
D
4.5 &1' 100
4.5 100
95.5 z 95.5
Therefore this cannot be the equation.
Substituting &1, 95.5' would result in 95.5 4.5 &1' 100
95.5
4.5 100
95.5 z 104.5
Therefore this cannot be the equation.
PTS: 1
TOP: 4.4
DIF: 2A
REF: CG p. 74,75
MSC: Linear Relations
3
OBJ: 9PR2
ID: A
4. ANS: C
(5, 7)
3x 2y
1
3(5) 2(7)
1
15 14
1
1
1
Feedback
A
(5, 8)
3x 2y
1
3(5) 2(8) z 1
15 16 z 1
31 z 1
B
(5, 7)
3x 2y
1
3(5) 2(7) z 1
15 14 z 1
29 z 1
C
D
Correct!
(5, 8)
3x 2y
1
3(5) 2(8) z 1
15 16 z 1
1z1
PTS: 1
TOP: 4.2
DIF: 2A
REF: CG p 74
MSC: Linear Relations
4
OBJ: 9PR2
ID: A
5. ANS: D
The line crosses the y-axis at -2.
Feedback
A
B
C
D
This is x 2
This is x 2
This is y 2
Correct!
PTS: 1
TOP: 4.3
6. ANS: A
s
DIF: 2M
REF: 9PR2
MSC: Linear Relations
OBJ: CG p 70
3n 2
When you create a table of values you can see that there is a constant change in both the independent
and dependent variables: as the figure number increases by 1, the number of sticks goes up by 3.
Also, if we observe the diagram we notice that 3 sticks are added each time. Therefore, the numerical
coefficient is 3.
If we notice that 3 sticks are added each time then the figure number always begins with the same 2
sticks - this is the constant term. We can observe this by using table below:
s
3n 2
Figure # (n) # of Sticks
(s)
1
5
2
8
3
11
4
14
5 3(1) 2
8 3(2) 2
11 3(3) 2
14 3(4) 2
Feedback
A
B
C
D
Correct!
Incorrent placement of the independent and dependent varaibles.
Incorrect constant term.
Incorrect constant term and incorrent placement of the independent and
dependent varaibles.
PTS: 1
TOP: 4.1
DIF: 2A
REF: CG p 66
MSC: Linear Relations
5
OBJ: 9PR1
ID: A
7. ANS: C
In figure number 1 the perimeter is 8, in figure number 2 the perimeter is 10, in figure number 3 the
perimeter is 12. It increases by 2 each time so the numerical coefficient must be 2. For figure number
1, 2 u 1 2 so we must add 6 to get to 8. This will work for figure number 2 and 3:
Figure 2-> 2(2) 6 10
Figure 3-> 2(3) 6 12
Therefore the equation is P
2n 6
Feedback
A
B
C
D
Used the increase of 2 as the constant instead of the numerical coefficient.
Added 4 instead of 6 because that is the perimeter of the square added in the
pattern each time.
Correct!
Used the perimeter in figure 1 as the constant.
PTS: 1
TOP: 4.1
8. ANS: A
DIF: 2A
REF: CG p.66
MSC: Linear Relations
OBJ: 9PR1
Although there is a constant change in x (increases by 1), there is not a constant change in y.
Increases by 3, then 5, then 7, then 9.
Feedback
A
B
C
D
Correct!
It is linear since there is a constant change in x (increases by 1) and y (increases
by 4).
It is linear since there is a constant change in x (increases by 1) and y (increases
by 5).
It is linear since there is a constant change in x (increases by 1) and y (decreases
by 1).
PTS: 1
TOP: 4.2
DIF: 2M
REF: CG p. 68
MSC: Linear Relations
6
OBJ: 9PR1
ID: A
9. ANS: A
Choose a point such as (1, 0) and check each equation. Check to see which equation satisifes this
point:
a. (1,0) -> y 3x 3 3(1) 3 0 Works!
b. (1,0) -> y x 3 1 3 2 Doesn’t work!
c. (1,0) -> y 3x 3(1) 3 Doesn’t work!
d. (1,0) -> y 3x 3 3(1) 3 6 Doesn’t work!
Note: If you choose the point (0,3) you will need to verify by choosing an additional point.
Feedback
A
B
C
D
Correct!
Student only verified with the point (0,3). Check with another point: (1,0) ->
y x 3 1 3 2 Doesn’t work!
Student only verified with the point (0,3). Check with another point: (1,0) ->
y 3x 3(1) 3 Doesn’t work!
Student only verified with the point (0,3). Check with another point: (1,0) ->
y 3x 3 3(1) 3 6 Doesn’t work!
PTS: 1
TOP: 4.4
10. ANS: C
x
DIF: 2A
REF: CG p.74
MSC: Linear Relations
OBJ: 9PR2
3 is a vertical line passing through the x-ais at 3
Feedback
A
B
C
D
May have thought lines have to have an x and y variable in the equation and
should be at the 3 location.
May have thought lines have to have an x and y variable in the equation and be
at the 3 location which is at the opposite of 3.
Correct!
May have thought that vertical line is associated with y variable.
PTS: 1
TOP: 4.3
DIF: 2M
REF: CG p.74
MSC: Linear Relations
7
OBJ: 9PR3
ID: A
SHORT ANSWER
11. ANS:
B matches graph 1 if we pick 2 points on the line and substitute into the equation to see if they
satisfy the equation.
Use &1, 1' and &0, 1' in 4x 2y 2
Both points work in the equation!
4(1) 2(1) 2
4(0) 2(1) 2
4 (2)
2
02
2
2
2
2
2
A matches graph 2 if we pick &1, 3' and &0, 1' and substitute in 4x y
4 &1' 3
1
4(0) (1)
1
43
1
01
1
1
1
1
1
PTS: 1
TOP: 4.4
1
Both points work in equation!
DIF: 3
REF: CG p. 74,75
MSC: Linear Relations
8
OBJ: 9PR2
ID: A
12. ANS:
a)
b)
Explanation – because I have to extend the line beyond the values given and I had to infer or estimate
the amount of savings at 30 weeks based on the linear trend in the known data.
PTS: 1
TOP: 4.5
DIF: 3
REF: CG p 76
MSC: Linear Relations
9
OBJ: 9PR2
ID: A
13. ANS:
Line A: y 2x
Line B: y x
4
1
Justification
Line (B) - Take any point on line and determine if equation is true such as (2,3)
y 3x
1
3 3(2)
1
36z 1
yx
1
y 2x
32
1
3 2(2)
1
1
4
4
34z 4
Correct!
Line (A) - Take any point on line and determine if equation is true such as (1,2)
y 3x
y 2x
1
2 3(1)
23z 1
PTS: 1
TOP: 4.4
1
4
2 2(1)
4
4
Correct!
4
DIF: 2A
REF: CG p 74
MSC: Linear Relations
10
OBJ: 9PR2
ID: A
14. ANS:
a)
Graph the data.
b) What should the chocolate maker charge for a 100g chocolate bar?
P (price), s(size)
P
s5
P
100 5
105 cents
It will cost $1.05 for a 100g chocolate bar.
c) What should be the size of a chocolate bar that costs $0.85?
P
s5
85 5
80
s55
s
An 80g bar will cost $0.85?
PTS: 1
TOP: 4.2,4.4
DIF: 2A
REF: CG p.70, 76
MSC: Linear Relations
11
OBJ: 9PR2