lines and linear equations

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46 Chapter 4 Test A

25 Suggested Time:

30 min

CHAPTER TEST A

Lines and Linear Equations4

Concepts and Skills (10 3 1 point 5 10 points)

Find the slope of each line.

1.

x

y

1 2 3 4 5

4

6

8

2

0

2.

x

y

1 2 3 4 5

4

6

8

2

0

Find the slope of the line passing through each pair of points.

3. A (4, 8) and B (2, 0) 4. P (0, 6) and Q (3, 0)

Use the given slope and y-intercept of a line to write an equation in slope-intercept form.

5. Slope, m 5 2 6. Slope, m 5 23 y-intercept, b 5 3 y-intercept, b 5 4

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Assessments Course 3 47

Write an equation of the line that passes through each given point and is parallel to y 5 23x 1 8.

7. (5, 2) 8. (0, 1)

Write an equation of the line with the given slope that passes through the given point.

9. Slope, m 5 21; (0, 2) 10. Slope, m 5 12

; (2, 21)

Problem Solving (Questions 11 to 13: 3 3 2 points 5 6 points Questions 14 to 16: 3 3 3 points 5 9 points)

Solve. Show your work.

11. Graph the line with slope, m 5 22 that passes through the point (21, 4) on the coordinate plane below.

x

y

�3 �2 �1�1

�2

1 2 3

1

1

�3

2

3

4

0

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48 Chapter 4 Test A

12. Two cable cars are descending from two separate stations. The altitude, y feet, of Cable Car A after x minutes is given by the equation y 5 230x 1 700. The graph shows the altitude, y feet, of Cable Car B after x minutes.

x

y

5 10 15 20

Time (min)

Altitude of Cable Car B

Alt

itud

e (f

t)

200

300

400

500

100

0

a) Which cable car is descending from a higher altitude?

b) Which cable car is descending at a faster rate?

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13. Car rental companies A and B each requires a deposit of D dollars, to rent a car, plus a fixed mileage charge.

x

y

10 20 30 40

Distance (mi)

Total Charges for Car Rental

Companies A and B

Dep

osi

t ($

)

50

Company B

Company A

20

30

40

10

0

a) Find the amount each car rental company requires for the deposit.

b) Which company charges a greater amount per mile?

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50 Chapter 4 Test A

14. Robert and Maria both work as chefs in a restaurant. After receiving their weekly paychecks, they each deposit a fixed amount into their respective bank accounts. The graph shows the amount of money in each of their accounts after one month.

x

y

1 2 3 4

Time (Wk)

Total Amount inBank Accounts

Dep

osi

t ($

) Maria

Robert

40

60

80

100

20

0

a) Which chef deposits the greater amount of money each week into his account? Explain what information you used to determine your answer.

b) In which week do the chefs have the same amount of money in their accounts?

c) Which chef started the month with more money? How can you tell?

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15. A holding tank for water is located underneath a leaking inlet valve. The tank initially contained a certain volume of water. The graph shows the total volume of water, y gallons, after x hours.

x

y

1 2 3 4

Time (h)

Total Volume ofWater in Holding Tank

Vo

lum

e (g

al)

5 6

2

3

4

5

1

0

a) Find the vertical intercept of the graph and explain what information it gives about the situation.

b) Find the slope of the graph and explain what information it gives about the situation.

c) If the maximum capacity of the holding tank is 4 gallons, predict approximately how many hours it will take for the tank to overflow.

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52 Chapter 4 Test A

16. Two molding machines, A and B, produce identical plastic mugs at different rates. The graph shows the mass of plastic, y pounds, needed to produce x number of mugs.

x

y

5 10 15 20

Number of Mugs

Plastic Needs forMolding Machines

Mas

s o

f P

last

ic (

lb)

25 30

10

15

20

25

30

5

0

Machine A

Machine B

a) At start-up, which machine requires the greater amount of plastic?

b) Which machine depletes its plastic more quickly?

c) Which machine uses the lesser amount of plastic per mug? Explain how you determine your answer.

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25 Suggested Time:

30 min

CHAPTER TEST B

Lines and Linear Equations4

Concepts and Skills (10 3 1 point 5 10 points)

Find the slope of each line.

1.

x

y

1 2 3 4 5

4

6

8

10

12

2

0

2.

x

y

1 2 3 4 5

4

6

8

10

12

2

0

Find the slope of the line passing through each pair of points.

3. M (3, 7) and N (1, 5) 4. H (0, 0) and K (3, 0)

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54 Chapter 4 Test B

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Use the given the slope and the y-intercept of a line to write an equation in slope-intercept form.

5. slope, m 5 34 6. slope, m 5 − 4

5

y-intercept 514

y-intercept 5 45

Write an equation of the line that passes through each given point and is parallel to 2y 5 26x 1 4.

7. (2, 0.5) 8. (0.8, 7)

Write an equation of the line with the given slope that passes through the given point.

9. Slope, m 5 3; (0, 23) 10. Slope, m 5 21; (21, 6)

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Problem Solving (Questions 11 to 13: 3 3 2 points 5 6 points, Questions 14 to16: 3 3 3 points 5 9 points)

Solve. Show your work.

11. Sketch the graph that passes through the point (2, 4) and has a slope of 2.

x

y

1 2 3 4 5 6

4

6

8

10

12

2

0

12. In an experiment, toy cars A and B are rolled down a slightly inclined plane. Each car starts at a different point from the top of the inclined plane. Car A’s distance, d feet, from the top of the inclined plane after x minutes is given by the equation d 5 0.5x 1 4. The graph shows Car B’s distance, d feet, from the top after x minutes.

a) Which car starts from a higher position on the inclined plane?

b) Which car rolls down the inclined plane at a faster rate?

x

d

5 10 15 20

Time (sec)

Distance Traveledby Toy Car B

Dis

tanc

e (f

t)

4

6

8

10

2

0

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56 Chapter 4 Test B

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13. Hot air balloon A rises y feet in x minutes. The equation representing its ascent is y 5 50x 1 5. The graph shows the altitude of hot air balloon B, y feet, after x minutes.

x

y

1 2

Time (min)

Altitude of Hot Air Balloon B

Hei

ght

(ft

)

3 4

100

200

300

400

500

0

a) Find the height of each balloon at time x 5 0.

b) Which balloon is moving at the greater rate? Justify your answer.

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14. Kelly conducted an experiment to find the effect of container surface color on the cooling temperature of water. Kelly filled two containers of the same shape and size, with the same volume of water. One container had a silver surface and the other had a dull-black surface. The graphs show the temperature of the water in each container, y °C, after x minutes.

a) Find the initial water temperature of both containers. Explain what information you use to determine your answer.

b) Which container has the greater rate in temperature change?

c) Write the equation to represent the change in temperature y in terms of time x for the silver container.

x

y

10 20

Time (min)

Dull-Black Container Silver Container

Temperatures of Water in aDull-Black Container and

Silver Container

Tem

per

atur

e (º

C)

30 40

30

40

50

60

0

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58 Chapter 4 Test B

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15. A car rental company charges an initial price of $100 plus a rate of $50 for every 10 miles it travels. The graph shows the charges for a car, C dollars after travelling for x miles.

x

C

10 20 30 40

Distance (mi)

Total Charges fora Car Rental

Co

st (

$)

50 60

200

300

400

100

0

a) Find the slope of the graph and explain what it means in the situation.

b) Write the equation in the slope-intercept form.

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16. A maintenance engineer turns on the relief valves of two pressure vessels in order to reduce the pressure within each vessel. The graphs show the change in vessel pressure, P in pounds per square inch, after x minutes.

x

y

2 4 6 8

Time (min)

Change in Vessel Pressureof Vessels A and B

Pre

ssur

e (lb

/100

0sq

ft)

10

2

3

4

5

6

1

0

Vessel B

Vessel A

a) Find the initial pressure of each vessel.

b) Predict how many minutes it will take for the pressure within the two vessels to measure the same.

c) Find the slope of each graph and explain what information it gives about the situation.

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16. a) A 5 100 1 0.1m b) Distance

Traveled (m miles)

Total Amount of Weekly Car Rental

(A dollars)150 1,115200 120250 125

Chapter 4 Pre-Test

1. No, constant of proportionality 5 1.2, y 5 1.2x 2. Yes, constant of proportionality 5 2, y 5 2x 3. No, constant of proportionality 5 22.5,

y 5 22.5x 4. Yes, constant of proportionality 5 22,

y 5 22x

Chapter 4 Test A

1. 25

2. �85

3. 4 4. 22

5. y 5 2x 1 3 6. y 5 23x 1 4

7. y 5 23x 1 17 8. y 5 23x 1 1

9. y 5 2x 1 2 10. � �y x 212

11.

x

y

�1

�2

�2�3 1 2 3�1

1

2

3

4

�3

0

12. a) Cable Car A b) Cable Car A

13. a) A charges $10 for deposit. B charges $20 for deposit. b) Company A charges a higher amount

per mile.

14. a) Robert’s deposit is $20. Tony’s deposit is $40.

b) Second week c) Maria: The vertical intercept of her

graph is greater.

5. 512

6. One solution, x 5 0

7. No solution 8. Infinite solutions

9. � � ��

y yx

86

; 83

10. y 5 18x 2 3; y 5 51

11. a) 2x 1 17 5 31 b) 14 years

12. a) 2x 1 1.5 b) 34 in.

13. a) C 5 40 1 1.5m b) $46

14. Length of Rectangle (w inches)

10 12 14 16 18

Area of Rectangle (S square inches)

110 108 98 80 54

15. a) y 5 200 2 200d b) Percent

Discount (d percent)

0.04 0.08 0.10

Discount Price (y dollars)

192 184 180

16. a) C 5 20 1 0.02n b) n 5 50(C – 20) c) 1,800

Chapter 3 Test B

1. �x 1811

2. x 5 5

3. �x 174

4. 115

5. 712

6. One solution, x 5 18

7. No solution 8. Infinite solutions

9. � � � �y x y3; 113

10. � � � �y x y7.5; 513

12

11. 30 years old

12. a) 4 ? 32d 1 3d 5 6d

b) Identity. They have the same solution.

13. a) P 5 (4w 1 10) b) 30 in.

14. a) 10 ft b) 2.5 1 4x 1 x 5 12.5 c) 8 ft

15. a) y 5 3x 2 0.5

b) $11

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224 Answers

c) Slope of vessel A 5 2300 lb/sq ft per min,

Slope of vessel B 5 2500 lb/sq ft per min.

Vessel A is dropping 300 lb/sq ft of pressure every minute while vessel B is dropping 500 lb/sq ft every minute.

Benchmark Test A for Chapters 3 and 4

1. B 2. C

3. D 4. D

5. A

6. a) x 5 22 b) x 5 2254

7. a) No solution, the equation is inconsistent. b) Infinite solutions. The equation is an

identity.

c) Infinite solutions. The equation is an identity.

8. 1.5; y 5 1.5x 1 3

9. a) x 21 0 1 2

y 1 4 7 10

b) x 21 0 1 2

y 1.5 2 2.5 3

10. a) No. The equation is of the form y 5 mx 1 c.

b) Yes. The equation is of the form y 5 mx. c) Yes. The equation is of the form y 5 mx. d) Yes. The equation is of the form y 5 mx.11. a) 12 mi/h b) 30 mi12. a) 3.5x 5 630 b) $27013. a) T 5 0.04t 1 30 b) 325 min14. The line has slope m 5 5. So, 5 plastic cups

produced per hour.

15. a) y 5 90 2 x b) x 5 33.5

16. a) $2; it represents the fixed cost to rent a bike.

b) The line has slope m 5 1. It represents the hourly rate to rent a bike.

c) $5

17. r: 2.8, 0.7; L: 18, 7.2; L 5 549

18. a) The line has slope m 5 212

. It represents

the temperature change per minute. b) Both canisters have the same

temperature change per minute since both lines have the same slope.

15. a) The vertical intercept is 3 gallons. It means that the tank holds 3 gallons of water initially.

b) The slope is 13. It means that the inlet

valve is leaking 13

gallon of water per hour.

c) After 3 hours, the tank will overflow.

16. a) Machine A b) Machine B c) Machine A uses lesser amount of plastic

per mug as its slope is less steep than the slope of Machine B.

Chapter 4 Test B

1. 0 2. undefined

3. 1 4. 0

5. � �y x34

14

6. � � �y x45

45

7. y 5 23x 1 6.5 8. y 5 23x 1 9.4

9. y 5 3x 2 3 10. y 52x 1 5

11.

0x

y

2

1

4

2

6

3 4 5 6

8

10

12

12. a) Toy car A b) Toy car A

13. a) Hot air balloon A: 5 ft Hot air balloon B: 500 ft

b) Hot air balloon B; Balloon A is ascending at a rate of 50 feet per minute, while Balloon B is descending at a rate of 100 feet per minute.

14. a) 65°C is taken from the vertical intercept for both graphs.

b) Dull-black container c) y 5 2x 1 65

15. a) The slope is $5 per mile the car travels. b) y 5 5x 1 100

16. a) Initial pressure of Vessel A: 5000 lb per sq ft

Initial pressure of Vessel B: 6000 lb per sq ft

b) after 5 minutes

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lines and linear equations

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