Name: ___________________________________ Date: _______________________________

…BLM 5.CR.1... (page 1)

Principles of Mathematics 9: Teacher’s Resource Copyright © 2006 McGraw-Hill Ryerson Limited. BLM 5.CR.1 Chapter 5 Review

Chapter 5 Review

5.1 Direct Variation, pages 238–245 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.

5.2 Partial Variation, pages 246–253 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

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?

5.3 Slope, pages 254–263 6. Find the slope of each line segment.

a) b)

Day 6

Name: ___________________________________ Date: _______________________________

…BLM 5.CR.1... (page 2)

Principles of Mathematics 9: Teacher’s Resource Copyright © 2006 McGraw-Hill Ryerson Limited. BLM 5.CR.1 Chapter 5 Review

7. Calculate the slope of each line segment.

a) EF b) GH c) JK

8. One endpoint of line segment AB is

A(3, 4). The slope of this line segment is

32 . Find possible coordinates for B.

5.4 Slope as a Rate of Change, pages 264–271 9. It took 8 min to fill a 52-L bucket.

a) What is the rate of change of the volume of water?

b) Graph the volume of water in the bucket over time.

10. Tom and Ana ran a race. The graph shows

the distance each person ran in 10 s.

Who ran faster? How much faster?

5.5 First Differences, pages 271–278 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?

5.6 Connecting Variation, Slope, and First Differences, pages 279–287

13. Represent the relation y = x + 2 using

numbers, a graph, and words.

Day 6

BLM Answers

BLM 5.6.1 Practice: Connecting Variation, Slope, and First Differences

1. a) 32

− b) 4 c) 432

+−= xy

2. a) 21 b) −2 c) 2

21

−= xy

3. a) partial variation b) −5 c) 3 d)

x y 0 −5 1 −2 2 1 3 4 4 7

e)

4. a)

b) The relationship between x and y is a partial variation. The initial value is −1 and the constant of variation is 4.

c) −1; 4; y = 4x − 1

5. a) Number of Toppings, n

Cost ($), C

0 8.00 1 8.50 2 9.00 3 9.50 4 10.00

b) c) C = 0.50n + 8.00 6. y varies partially with x, the initial value is −2 and

the constant of variation is 43

−

x y −4 1 0 −2 4 −5

243

−−= xy

BLM 5.CR.1 Chapter 5 Review 1. a)

b) 21 c) xy

21

=

2. a) Time, t Earnings, E

0 0 1 7 2 14 3 21 4 28

Solutions for "Chapter 5 Review" Day 6

BLM Answers

b) c) 7; the amount Evan earns each hour he babysits d) y = 7x 3. a) direct variation b) neither c) partial variation d) partial variation 4. a) 1; 5 b) y = 5x + 1 c)

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

6. a) 52

− b) 5

7. a) 56

b) 37

− c) 310

8. Answers may vary. Possible answer: B(6, 6) 9. a) 6.5 L/min b) 10. Tom; 1 m/s 11. a) linear b) linear 12. a)

Side Length Perimeter 1 4 2 8 3 12 4 16 5 20

b) linear 13.

x y 0 2 1 3 2 4 3 5 4 6

The length of a rectangle is 2 more than its width.

Day 6Solutions for "Chapter 5 Review"