Unit 05 Celebration Practice
Multiple Choice
D y = 2x – 5
C y = 5x2
For each question, select the best answer.
1. Which relation is a direct variation?
A y = 5x
B y = 2x
C y = 5x2
D y = 5x – 2
2. The cost of tea varies directly with the
mass. Liz bought 4.5 kg of tea for $10.35.
What is the constant of variation?
A 0.43
B 14.85
C 5.85
D 2.30
3. What is the slope of this ramp?
7. Sophie’s earnings vary directly with the
number of hours she works. She earned
$25 in 4 h. What is the constant of
variation?
A 0.16
B 6.25
C 100
D 21
8. What is the slope of this staircase?
A 6
B
3
2
C 2
D
2
3
9. Which equation represents this relation?
A 2
2
B
9
C 18
D
9
2
4. Which equation represents this relation?
x
y
0
4
1
1
2
–2
3
–5
4
–8
A y = –3x + 4
C y = 3x + 4
B y = 4x – 3
D y = 3x – 4
Which relation is a partial variation?
A y = 25x
y
–1
–3
–5
–7
–9
A y = –x – 2
B y = 2x – 1
C y = –2x – 1
D y = 2x + 1
10. The cost to cater a party is $200 plus
$15 for each guest. Which equation
represents this relation?
5. The cost of a newspaper advertisement is
$750 plus $80 for each day it runs. Which
equation represents this relation?
A C = 80n – 750
B C = 80n + 750
C C = 750n + 80
D C = 750n – 80
6.
x
0
1
2
3
4
B y = 2x
A C = 15n + 200
B C = 15n – 200
C C = 200n + 15
D C = 200n – 15
Direct Variation
1. a) Graph the data in the table.
x
y
0
0
1
0.5
2
1.0
3
1.5
4
2.0
5
2.5
b) What is the constant of variation for
this relationship?
c) Write an equation relating y and x.
2. Evan earns $7/h babysitting. The amount
he earns, in dollars, varies directly with
the time, in hours, he babysits.
a) Assign variables. Make a table of
values showing Evan’s earnings for 0
h, 1 h, 2 h, 3 h, and 4 h.
b) Graph the relationship.
c) Identify the constant of variation.
What does this represent?
d) Write an equation in the form y = kx.
$1500. Printing costs $0.08 per brochure.
The relationship between cost and the
number of brochures is a partial variation.
a) Identify the fixed cost and the variable
cost.
b) Write an equation for this relationship.
c) What is the total cost for 800 brochures?
Slope
6. Find the slope of each line segment.
a)
b)
Partial Variation
3. Classify each relation as a direct variation,
a partial variation, or neither. Explain.
a) d = 45t
b) y = 2x2 + 3
c) y = 2x + 3
d) d = 45t + 12
4. The relationship between the variables in
the table is a partial variation.
x
y
0
1
1
6
2
11
3
16
4
21
5
26
7.
Calculate the slope of each line
segment.
a) Identify the initial value of y and the
constant of variation.
b) Write an equation in the form
y = mx + b.
c) Graph the relation. Describe the graph.
5. The owner of a small business is having
brochures printed. The design cost is
a) EF
b) GH
c) JK
8. One endpoint of line segment AB is
A(3, 4). The slope of this line segment
Short Response
1. a) Calculate the slope.
2
is . Find possible coordinates for B.
3
Slope as a Rate of Change,
10. Tom and Ana ran a race. The graph shows
the distance each person ran in 10 s.
b) Find the vertical intercept.
c) Write an equation for the relation.
2. The cost to ship goods varies directly with
the mass. Paul paid $20.40 to ship a
package with mass 24 kg. Write an
equation for this relationship.
Who ran faster? How much faster?
First Differences
11. Use first differences. Is each relation
linear or non-linear?
a)
b)
x
y
x
y
0
–1
0
0
1
2
1
–2
2
5
2
–4
3
8
3
–6
4
11
4
–8
5
14
5
–10
12. a) Make a table comparing the side
length of a square to its perimeter for
side lengths 1, 2, 3, 4, and 5.
b) Is the relationship between side length
and perimeter linear or non-linear?
3. Is this relation linear or non-linear? How
can you tell without graphing?
x
y
2
0.16
4
0.64
6
1.44
8
2.56
4. Sheila works in a bookstore. She earns
$240 per week, plus $0.15 for every
bestseller she sells.
a) Write an equation for this relationship.
b) Last week, Sheila sold 19 bestsellers.
How much did she earn?
5.
This graph shows the volume of water in a
child’s pool over time as the pool is
draining.
8. Is this relation linear or non-linear? How
can you tell without graphing?
x
y
4
8.4
8
16.8
12
25.2
16
33.6
9. The cost to install wood trim is $50, plus
$6/m of trim installed.
a) Write an equation for this relationship.
b) 18 m of trim were installed. What was
the total cost?
10. This graph shows the relationship
between the cost of a taxi trip and the
length of
the trip.
a) Calculate the rate of change of the
volume of water. How does the rate of
change relate to the graph?
b) Write an equation for the relationship.
c) Suppose the rate of change changes to
–4 L/min. How long will it take the
pool to empty?
6. a) Calculate the slope.
a) Calculate the rate of change of cost.
How does the rate of change relate to
the graph?
b) Write an equation for the relationship.
c) Suppose the flat fee changed to $3.00.
How would the equation change?
How would the graph change?
b) Find the vertical intercept.
c) Write an equation for the relation.
7. The distance travelled varies directly with
time. Anthony ran 49.6 m in 8 s.
a) Write an equation for this relationship.
b) Graph the relation.
Answer key
Partial Variation
3. a) direct variation
b) neither
c) partial variation
d) partial variation
4. a) 1; 5
b) y = 5x + 1
c)
Multiple Choice:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
D
B
A
B
D
B
D
C
A
Direct Variation:
1. a)
b)
1
2
c) y =
1
x
2
2. a)
Time, t
0
1
2
3
4
Earnings, E
0
7
14
21
28
b)
The graph intersects the y-axis at (0, 1).
As the x-values increase by 1, the y-values
increase by 5.
5. a) fixed cost: $1500
variable cost: $0.08 times the number of
brochures
b) C = 0.08n + 1500
c) $1564
Slope:
6. a) -
2
5
b) 5
7. a) 5
b)  3
c) 3
6
7
10
8. Answers may vary. Possible answer:B(6, 6)
c) 7; the amount Evan earns each hour he babysits
d) y = 7x
9. a) 6.5 L/min
b)
3. Non-linear; I found the first differences and
noticed they were not equal.
4. a) E = 0.15n + 240 b) $242.85
5. a) 3 L/min; the rate of change is the slope
b) V = 200  3t
c) 50 min
3
b) 6
7
7. a) d = 6.2t
b)
6. a) -
c) y = -
3
x+6
7
Slope as a rate of change:
10. Tom; 1 m/s
First Differences:
11. a) linear
b) linear
12. a)
Side Length
1
2
3
4
5
b) linear
Perimeter
4
8
12
16
20
Short Response:
1. a)
3
2
b) 3
2. C = 0.85m
c) y =
3
x -3
2
8. Linear; I found the first differences and noticed
they were all equal.
9. a) C = 6l + 50
b) $158
10. a) $0.95/km; the rate of change is the slope
b) C = 0.95d + 2.50
c) The fixed portion of the equation would change
from 2.50 to 3.00. The graph would shift up so
the vertical intercept is 3.
Review – Slope Part I…
1) a)
X
Y
-5
38
8
- 53
11
- 74
-9
66
- 14
101
b) y = - 7x + 3
c) Partial, because it does not go through the origin
2.
3) a) The slope between all points is
−1
2
, therefore all points are collinear
9
b) The slope between all points works out to be 2, therefore they are all collinear.
4. a) y = 3x + 7
1
b) y = 5x+2
2
c) y = 3 𝑥 − 8
d) y = 10x – 6
5. They are all partial variation because they all have a y-intercept and do not go through the origin.