Objective 3: the Student Will Demonstrate an Understanding of Linear Functions

Objective 3: The student will demonstrate an understanding of linear functions.

A.5A The student is expected to determine whether or not given situations can be represented by linear functions.

1. (A.5A, 09-12, 10) The tables below show the amount of data in kilobytes that was downloaded by a computer over time. Which of the following tables best represents a linear function?
A
Kilobytes Downloaded
Time (seconds) / Number of Kilobytes
10 / 65
20 / 130
30 / 180
40 / 215
/ C
Kilobytes Downloaded
Time (seconds) / Number of Kilobytes
10 / 35
20 / 80
30 / 125
40 / 150
B
Kilobytes Downloaded
Time (seconds) / Number of Kilobytes
10 / 40
20 / 80
30 / 110
40 / 140
/ D ß
Kilobytes Downloaded
Time (seconds) / Number of Kilobytes
10 / 45
20 / 90
30 / 135
40 / 180
/ 4. (A.5A) Which problem situation can not be described by a linear function?
A The distance an object falls is proportional to the square of the length of time that it has been falling. ß
B The cost of tree removal is proportional to the size of the tree.
C The relationship between the volume of a cylinder and its height, as long as the radius of the cylinder remains constant.
D The perimeter of an equilateral triangle in relation to the length
of the side(s) of the triangle.
5. (A.5A) The graph of which of the following would show a linear relationship?
A The number of roses ordered daily from May 1st to May 31st.
B The distance covered by a motorcycle going across Rocky Mountain recorded every 10 minutes.
C The number of candles on a person’s birthday cake every year. ß
D The number of bathing suits bought each month from January
to December.
2. (A.5A, 05-2, 11) Identify the situation that best represents the amount in the function .
A Simon Cowell paid $75 each for n gifts and spent $80 on himself.
B Silver on 90210 spent $75 on registration fees and $80 each for n credit hours last semester. ß
C Charlie on Two and a Half Men deposited $75 per month for n months and an extra $80 in the summer.
D Carlos Mencia worked for 75 hours at n dollars per hour and earned $80 in tips. / 6. (A.5A, 06-42, 11) Cedric the Entertainer bought a package of 36 tickets for carnival rides. Each ride requires 4 tickets per person. Which linear function, if any, represents the relationship between x, the number of carnival rides Cedric went on, and y, the number of tickets remaining?
A
B
C ß
D No linear function exists.
3. (A.5A) Which table represents a linear function?
A
x / y
3 / 8
–2 / 3
4 / –1
/ C ß
x / y
8 / 1
4 / –1
–6 / –6
B
x / y
5 / –2
–1 / 2
0 / 0
/ D
x / y
1 / 1
2 / 2
3 / –3
/ 7. (A.5A) Which table represents a linear relationship?
A
x / y
–1 / 1
0 / 0
2 / 4
/ C
x / y
2 / 11
–1 / –5
–3 / 21
B ß
x / y
–3 / –4
–1 / –1
7 / 11
/ D
x / y
–8 / –31
–4 / –11
0 / 1

A.5C The student is expected to use, translate, and make connection among algebraic, tabular, graphical, or verbal descriptions of linear functions.

1. (A.5C, 09-46, 9) Which graph best represents the function ?
A C

B ß D
/ 4. (A.5C, 09-38, 10) Which of the following best represents the graph of the equation ?
A ß C

B D

2. (A.5C, 08-1, 10) Which equation best represents the line graphed below?

A C
B ß D / 5. (A.5C, 09-28, 11) Which equation best represents the line graphed below?

A C
B ß D.
3. (A.5C, 04-13, 9) Which function includes the data set
{(2, 4), (6, 6), (12, 9)}?
A
B
C
D ß / 6. (A.5C, 04-40, 11) Which equation best represents the line on the graph?

A
B
C ß
D

A.5C The student is expected to use, translate, and make connection among algebraic, tabular, graphical, or verbal descriptions of linear functions.

7. (A,5C, 06-55, 10) Which table best describes points on the line graphed below?

A C ß

B D
/ 8. (A.5C, 04-52, 10) Which graph best represents the
function ?
A C

B D ß

A.6A The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations.

1. (A.6A, 04-19, 9) What is the slope of the linear function shown in the graph?

A C
B ß D / 2. (A.6A, 04-26, 10) What is the rate of change of the graph below?

A 0.6 ß
B 1.67
C 3.5
D –1.67

A.6A The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations.

3. (A.6A, 08-1, 9) What is the slope of the line described by the equation ?
A ß C
B D / 7. (A.6A, 09-34, 10) What is the slope of the graph of the equation ?
A C
B ß D
4. (A.6A, 06-17, 9) What is the slope of the line that contains the coordinate points (8, –3) and (–2, 7)?

A ß C
B D / 8. (A.6A, 08-1, 11) Which of the following tables best represents a linear function with a rate of change of ?
A C

B ß D

5. (A.6A, 09-52, 11) What is the slope of the linear equation ?
A –101 C ß
B D / 9. (A.6A, 06-52, 11) What is the rate of change of the function ?
A 7
B –7
C 0 ß
D Undefined
6. (A.6A, 06-52, 11) What is the slope of the function ?
A
B –3 ß
C –4
D 3 / 10. (A.6A, 06-15, 11) What is the apparent slope of the line graphed below?

A C
B D ß

A.6A The student is expected to develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations.

11. (A.6A, 06-40, 10) Which line appears to have a slope of zero?

A Line n
B Line k
C Line wß
D Line p / 12. (A.6A, 06-40, 10) Which line appears to have no slope?

A Line n
B Line k
C Line w
D Line pß

A.6B The student is expected to [collect and] organize data, [make and] interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

1. (A.6B, 08-2, 11) Some employees of Ace Corporation left their office building and drove separately on the same road to a convention. The graph shows the distance traveled by each employee after 5 hours of nonstop driving at 4 different speeds.

Which employee drove at the slowest rate to the convention?
A Mr. Able
B Ms. Ruiz ß
C Ms. Woo
D Mr. Hill / 2. (A.6B) Some employees of Ace Corporation left their office building and drove separately on the same road to a convention. The graph shows the distance traveled by each employee after 5 hours of nonstop driving at 4 different speeds.

Which employee drove at the fastest rate to the convention?
A Mr. Able
B Ms. Ruiz
C Ms. Woo ß
D Mr. Hill

3. (A.6B, 08-2, 9) The cost of renting a car for 1 day at Hertz is $20 plus 10 cents per mile driven. The cost of renting a car for 1 day at Enterprise is $20 plus 15 cents per mile driven. In a graph of the cost of a car rental, what does the cost per mile driven represent?
A The x-intercept
B The y-intercept
C The slope ß
D The point of intersection / 6. (A.6B) The cost of renting a car for 1 day at Hertz is $20 plus 10 cents per mile driven. The cost of renting a car for 1 day at Enterprise is $20 plus 15 cents per mile driven. In a graph of the cost of a car rental, what does the $20 represent?
A The x-intercept
B The y-intercept ß
C The slope
D The domain
4. (A.6B, 06-11, 9) A small business purchased a van to handle its delivery orders. The graph below shows the value of this van over a period of time. Which of the following best describes this situation?

A The van was purchased for $1,600.
B The van decreases in value by $1,600 per year. ß
C The van increases in value by $1,600 per year.
D The van has no value after 5 years. / 7. (A.6B, 04-34, 9) The line segment on the graph shows the altitude of a landing airplane from the time its wheels are lowered to the time it touches the ground. Which of the following best describes the slope of the line segment?

A The plane descends about 1 foot per 8 seconds.
B The plane descends about 8 feet per second. ß
C The plane descends about 1 foot per 2 seconds.
D The plane descends about 2 feet per second.
5. (A.6B, 06-12, 10) The graph shows the distance a certain motorbike can travel at a constant speed with respect to time. Which of the following best describes the meaning of the slope of the line representing this situation?

A The motorbike travels at a speed of about 8 miles per hour.
B The motorbike travels at a speed of about 2.5 miles per hour.
C The motorbike travels at a speed of about 5 miles per hour.
D The motorbike travels at a speed of about 10 miles per hour. ß / 8. (A.6B) The graph below shows the number of pies and the number of cakes that the students in the art club need to sell at the school bake sale in order to raise $150. Which of the following represents the maximum number of cakes the art club could sell to raise exactly $150?

A 40
B 25
C 50
D 30ß

A.6C The student is expected to investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b.

1. (A.6C, 09-4, 9) The original function is graphed on the same grid as the new function. Which of the following statements about these graphs is true?
A The graph of the original function is steeper than the graph of the new function.
B The graph of the original function is parallel to the graph of the new function.
C The graphs intersect at (4, 0).
D The graphs intersect at (0, 4). ß / 3. (A.6C, 05-31, 11) If the slope of the function is changed to 1.5, which of the following best describes the graph of the new function?
A The graph of the new function intercepts the y-axis at the same point as the original function. ß
B The graph of the new function intercepts the x-axis at the same point as the original function.
C The graph of the new function has a negative slope.
D The graph of the new function has a positive
x-intercept.
2. (A.6C, 06-12, 9) The graph of a linear function is shown on the coordinate grid below.

If the y-intercept is changed to (0, 5) and the slope becomes -4, which statement best describes the relationship between the two lines when they are graphed on the same coordinate grid?
A The y-intercepts are 1 unit apart, and the lines are parallel.
B The y-intercepts are 1 unit apart, and the lines intersect at (1, 1). ß
C The y-intercepts are 1 unit apart, and the lines are perpendicular.
D The y-intercepts are 1 unit apart, and the lines intersect at (1, 0). / 4. (A.6C, 04-8, 10) What will happen to the slope of line p if the line is shifted so that the y-intercept increases and the
x-intercept remains the same?

A The slope will change from positive to negative.
B The slope will change from negative to positive.
C The slope will increase. ß
D The slope will decrease.

A.6C The student is expected to investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b.

5. (A.6C, 09-18, 11) The function is graphed below.

In the function above, the slope will be multiplied by –2, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function?
A C

B D ß
/ 6. (A.6C, 08-2, 10) Which best describes the effect on the x-intercept of the graph of if the slope is changed to ?

A The x-intercept remains the same, and the new line is translated upward.
B The x-intercept becomes negative, and the new line is parallel to the original line.
C The x-intercept remains the same, and the new line is translated downward.
D The x-intercept becomes negative, and the new line intersects the original line. ß

A.6D The student is expected to graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y intercept.