Unit 05 Celebration Practice

Multiple Choice

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?

A 2 B29

C 18 D92

 4. Which equation represents this relation?

x y0 41 12 –23 –54 –8

A y = –3x + 4 B y = 4x – 3C y = 3x + 4 D y = 3x – 4

 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 + 750C C = 750n + 80 D C = 750n – 80

6. Which relation is a partial variation?A y = 25x B y = 2x

C y = 5x2 D y = 2x – 5

 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 6.25C 100 D 21

 8. What is the slope of this staircase?

A 6 B32

C 2 D23

 9. Which equation represents this relation?x y0 –11 –32 –53 –74 –9

A y = –x – 2 B y = 2x – 1C 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?

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 y0 01 0.52 1.03 1.54 2.05 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.

Partial Variation 3. Classify each relation as a direct variation,

a partial variation, or neither. Explain.a) d = 45t b) y = 2x2 + 3c) y = 2x + 3 d) d = 45t + 12

 4. The relationship between the variables in the table is a partial variation.x y0 11 62 113 164 215 26

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

$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)

 7. Calculate the slope of each line segment.

Principles of Mathematics 9: Teacher’s Resource Copyright © 2006 McGraw-Hill Ryerson Limited.BLM 5.4.2 Achievement Check Rubric2

a) EF b) GH c) JK

 8. One endpoint of line segment AB is A(3, 4). The slope of this line segment

is 23 . Find possible coordinates for B.

Slope as a Rate of Change,

10. Tom and Ana ran a race. The graph shows the distance each person ran in 10 s.

Who ran faster? How much faster?

First Differences

11. Use first differences. Is each relation linear or non-linear?a) b)

x y x y0 –1 0 01 2 1 –22 5 2 –43 8 3 –64 11 4 –85 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?

Short Response

 1. a) Calculate the slope.

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.

 3. Is this relation linear or non-linear? How can you tell without graphing?x y2 0.164 0.646 1.448 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.

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.

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.  8. Is this relation linear or non-linear? How

can you tell without graphing?x y 4 8.4 8 16.812 25.216 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 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?

Principles of Mathematics 9: Teacher’s Resource Copyright © 2006 McGraw-Hill Ryerson Limited.BLM 5.4.2 Achievement Check Rubric4

Answer keyMultiple Choice: 1. A 2. D 3. B 4. A 5. B 6. D 7. B 8. D 9. C 10. A

Direct Variation: 1. a)

b)

12 c)

y = 12

x

 2. a)Time, t Earnings, E

0 01 72 143 214 28

b)

c) 7; the amount Evan earns each hour he babysitsd) y = 7x

Partial Variation 3. a) direct variation

b) neitherc) partial variationd) partial variation

 4. a) 1; 5b) y = 5x + 1c)

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: $1500variable cost: $0.08 times the number of brochures

b) C = 0.08n + 1500c) $1564

Slope: 

6. a)−2

5 b) 5

 7. a) b) c) 8. Answers may vary. Possible answer:B(6, 6)

 9. a) 6.5 L/minb)

Slope as a rate of change:10. Tom; 1 m/s

First Differences:11. a) linear

b) linear12. a)

Side Length Perimeter1 42 83 124 165 20

b) linear

Short Response:

 1. a)

32 b) 3 c)

y = 32

x −3

 2. C = 0.85m 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 3tc) 50 min

 6. a)− 3

7 b) 6 c)y =−3

7x + 6

 7. a) d = 6.2tb)

 8. Linear; I found the first differences and noticed they were all equal.

 9. a) C = 6l + 50b) $158

10. a) $0.95/km; the rate of change is the slopeb) C = 0.95d + 2.50c) 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.

Principles of Mathematics 9: Teacher’s Resource Copyright © 2006 McGraw-Hill Ryerson Limited.BLM 5.4.2 Achievement Check Rubric6

Review – Slope Part I…1) a)

X Y- 5 388 - 5311 - 74- 9 66- 14 101

b) y = - 7x + 3c) Partial, because it does not go through the origin

2.

3) a) The slope between all points is −12 , therefore all points are collinear

b) The slope between all points works out to be 92 , therefore they are all collinear.

4. a) y = 3x + 7

b) y = 15x+2

c) y = 23

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.

Principles of Mathematics 9: Teacher’s Resource Copyright © 2006 McGraw-Hill Ryerson Limited.BLM 5.4.2 Achievement Check Rubric8