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Mid-Unit Test REVIEW – Linear Functions

1. Each of the four graphs below was made with a motion detector.

A B

C D

a. Which graph best represents this situation: Carl ran toward the motion detector at a constant rate and then forgot what he was doing and stood still. Then he walked away from the motion detector. Explain your choice.

b. Which graph best represents this situation: Sally stood still. Explain your choice.

Unit 4 Mid-Unit Test REVIEW CT Algebra I Model Curriculum Version 3.0

Graph B best represents this situation. As Carl runs toward the motion detector, the line is steep and decreasing. As Carl stands still, his distance is not changing. Therefore the line will be horizontal. As Carl walks away, the line will be less steep and increasing.

Graph A best represents this situation because standing still will cause her distance to the motion detector to remain the same. Therefore the line will be horizontal.

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2. A full 180-gallon pool is being emptied with water from a hose. The water comes out at a constant rate of 6 gallons per minute. The volume of water in the pool is a function of time. a. Complete the following table.

Time (in minutes) Volume of Water (in gallons)

0 180 2 4 6 8

b. Graph the function. Make sure to label and scale your axes.

c. Is this an increasing or a decreasing function?

d. What is the rate of change or slope for the function? Specify the units.

e. What is the y -intercept of the function?

f. Write the equation of this function in form.xy = m + b

g. How long will it take for the pool to completely empty with water? Show your work.

Unit 4 Mid-Unit Test REVIEW CT Algebra I Model Curriculum Version 3.0

(The volume of the pool decreases at a rate of 6 gallons per minute.)

At 0 minutes, the volume of the pool is 180 gallons.

It will take 30 minutes for the pool to empty.

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3. Francis is making fried dough at the Woodstock Fair. He initially had 52 pieces at the

beginning of the day. Every minute he makes 4 pieces of fried dough. The amount of fried dough which Francis has is a function of time.

a. Is this an increasing or a decreasing function?

b. What is the rate of change or slope for the function? Specify the units.

c. What is the y -intercept of the function?

d. Write the equation of this function in form.xy = m + b

e. How long will it take Francis to have 300 pieces of fried dough? Show your work. 4. Match the function on the left with its identical representation on the right.

Note : One function on the left will not be used.

A. xy = ½ − 4

B. xy = 2 + 4

C. xy = ½ − 1

D. x y 0 75 1 65 2 55 3 45 4 35 5 25

W. Kassadee spends $10 each day on lunch. She starts the school year with $75.

X. An aloe plant has a stem that is 4 inches long. Each month, the stem grows another 2 inches.

Y.

Unit 4 Mid-Unit Test REVIEW CT Algebra I Model Curriculum Version 3.0

Francis makes 4 pieces of fried dough every minute.

Francis started with 52 pieces of fried dough.

It will take Francis 62 minutes (one hour and two minutes) to have 300 total pieces of fried dough.

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5. Use the coordinate plane below.

a. What is the y-intercept for this line? b. What is the slope of this line? f. Write the equation of this line in form.xy = m + b

c. Draw a line that is parallel to this line on the coordinate plane. d. Write the equation of your parallel line in form.xy = m + b

Unit 4 Mid-Unit Test REVIEW CT Algebra I Model Curriculum Version 3.0

Your answer may be different. The m value should still be -3 while the b value can be anything besides 1.

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6. Use the coordinate plane below.

a. Place a point on (-5, -3) and label it point A. b. Draw a horizontal line through the point (-5, -3). What is the equation of this horizontal

line?

c. Draw a vertical line through the point (-5, -3). What is the equation of this vertical line?

d. Place a point on (6, -4) and label it point D. Draw a line through (-5, -3) and (6, -4).

e. Find the slope of the line through the two points (-5, -3) and (6, -4). Explain how you found it.

f. What is the slope of a line that is perpendicular to the line drawn through (-5, -3) and (6, -4).

Unit 4 Mid-Unit Test REVIEW CT Algebra I Model Curriculum Version 3.0