Deck 8: The Slope of a Line

Question 1

Determine if the following table could represent ordered pairs from an equation of a line. x y 0 2 1 4 2 6 3 8

A) yes
B) no

Answer 1

A

Question 2

Find the slope of the line from the graph.

A) 2
B) -1
C) 0
D) 1
E) no slope

Answer 2

E

Question 3

Find the slope of the line through the pair of points (1, 0) and (3, 3). Then, plot the points, draw a line through them, and indicate the rise and run on the graph.

A)
B)
C)
D)

Answer 3

A

Question 4

Line l contains the points (4, - 6) and (4, 3). Give the slope of any line perpendicular to l .

Question 5

Find the slope of the line through the pair of points (1, 6) and (5, 4). Then, plot the points, draw a line through them, and indicate the rise and run on the graph.

A)
B)
C)
D)

Question 6

Line l contains the points (1, - 9) and (1, 4). Give the slope of any line perpendicular to l .

A) 2
B) - 1
C) 0
D) 3
E) no slope

Question 7

Find the slope of the line from the graph.

Question 8

Graph the line that has an x -intercept of 4 and a y -intercept of - 3. What is the slope of this line?

A)
B)
C)
D)

Question 9

Find the slope of the line from the graph.

A)
B)
C)
D)
E) no slope

Question 10

Solve for .

A)
B)
C)
D)
E)

Question 11

Find the slope of the line from the graph.

A)
B)
C)
D)
E) no slope

Question 12

Find the slope of the line through the pair of points (- 4, 3) and (4, - 3). Then, plot the points, draw a line through them, and indicate the rise and run on the graph.

A)
B)
C)
D)

Question 13

Which line has a positive slope?

A) A, B, C
B) D, B
C) A, C
D) B, C
E) B, C, D

Question 14

Find the slope of the line through the pair of points (- 2, - 6) and (2, 3). Then, plot the points, draw a line through them, and indicate the rise and run on the graph.

A)
B)
C)
D)

Question 15

Find the slope of any line parallel to the line through (14, 18) and (- 4, 14).

A)
B)
C)
D)
E)

Question 16

Graph the line that has an x -intercept of 4 and a y -intercept of 2. What is the slope of this line?

A)
B)
C)
D)

Question 17

Line l contains the points (9, 4) and (-9, 3). Give the slope of any line perpendicular to l .

Question 18

Line l contains the points (6, 2) and (- 6, 1). Give the slope of any line perpendicular to l .

A)
B)
C)
D)
E) no slope

Question 19

Find the slope of the line from the graph.

A) 4
B) 5
C) -5
D) 0
E) no slope

Question 20

Which line has a positive slope?

Question 21

Give the slope and y -intercept of y = - 2. Sketch the graph.

A) Slope = 0 y -intercept = 2
B) Slope = 0 y -intercept = - 2
C) Slope = 2 y -intercept = 0
D) no slope y -intercept = - 2
E) no slope y -intercept = 2

Question 22

Write the equation of the line with the slope m = - 9 and y -intercept b = - 5.

A) y = 9 x + 5
B) y = - 5 x - 9
C) y = -5 x + 9
D) y = 5 x + 9
E) y = - 9 x - 5

Question 23

Give the slope and y -intercept for the following equation. Sketch the graph using the slope and y -intercept. Give the slope of any line perpendicular to the given line.

A) Slope = y -intercept = perpendicular slope =
B) Slope = y -intercept = perpendicular slope =
C) Slope = y -intercept = perpendicular slope =
D) Slope = y -intercept = perpendicular slope =

Question 24

Find the slope of the line from the graph.

Question 25

Find the equation of the line that passes through the pair of points (5, 6) and (- 3, - 2). Write your answer in standard form.

A)
B)
C)
D)
E)

Question 26

Find the equation of the line parallel to the graph of 4 x - y = 5 that contains the point (- 3, 1).

A)
B)
C)
D)
E)

Question 27

The slope of the line is m = 3 and one point on a line is (- 1, - 6). Find the equation of the line and write the answer in slope-intercept form.

A)
B)
C)
D)
E)

Question 28

Write the equation of the line with the slope and y -intercept

A)
B)
C)
D)
E)

Question 29

Write the equation of the line with the slope m = 7 and y -intercept b = 9.

A) y = 7 x + 9
B) y = 9 x + 7
C) y = 7 x - 9
D) y = -9 x - 7
E) y = 9 x - 7

Question 30

Give the slope and y -intercept for the following equation. Sketch the graph using the slope and y -intercept. Give the slope of any line perpendicular to the given line.

A) Slope = y -intercept = perpendicular slope =
B) Slope = y -intercept = perpendicular slope =
C) Slope = y -intercept = perpendicular slope =
D) Slope = y -intercept = perpendicular slope =

Question 31

For the following line, name the slope and y -intercept. Then write the equation of the line in slope-intercept form.

A)
B)
C)
D)
E)

Question 32

For the line x = - 2, sketch the graph, give the slope, and name any intercepts.

A) Slope = 0 y -intercept = 2 no x -intercepts
B) Slope = 2 y -intercept = 0 x -intercept = 0
C) Slope = 0 y -intercept = - 2 no x -intercepts
D) no slope x -intercept = - 2 no y -intercepts
E) no slope x -intercept = 2 no y -intercepts

Question 33

The slope of the line is and one point on a line is . Find the equation of the line and write the answer in slope-intercept form.

A)
B)
C)
D)
E)

Question 34

Determine if each of the following tables could represent ordered pairs from an equation of a line.

Question 35

Find the equation of the line that passes through the pair of points. Write your answer in standard form.

A)
B)
C)
D)
E)

Question 36

Find the slope of any line parallel to the line through (7, 5) and (- 2, 4).

Question 37

Solve for .

Question 38

Write the equation of the line with the slope m = 0 and y -intercept b = 5.

A) y = 5
B) y = 5 x + 5
C) y = 5 x
D) x = 5 y
E) x = 5

Question 39

Find the slope of the line from the graph.

Question 40

Find the slope of the line from the graph.

Question 41

The slope of the line is m = 5 and one point on a line is (- 1, - 8). Find the equation of the line and write the answer in slope-intercept form.

Question 42

Give the equation of the line perpendicular to the graph of that has an -intercept of .

A)
B)
C)
D)
E)

Question 43

Give the equation of the line perpendicular to the graph of that has an -intercept of .

Question 44

Write the equation of the line with the slope m = 0 and y -intercept b = 5.

Question 45

In an aerobics class, the instructor indicates that her students' exercise heart rate is 55% of their maximum heart rate, where maximum heart rate is 220 minus their age. Determine the equation that gives exercise heart rate E in terms of age A .

A)
B)
C)
D)
E)

Question 46

The slope of the line is and one point on a line is . Find the equation of the line and write the answer in slope-intercept form.

Question 47

Find the equation of the line that passes through the pair of points (1, 7) and (- 8, - 2). Write your answer in standard form.

Question 48

To produce this textbook, suppose the publisher spent $125,000 for typesetting and $3.50 per book for printing and binding. The total cost to produce and print n books can be written as Total cost to produce n textbooks = Fixed cost + Variable cost = Suppose the number of books printed in the first printing is 10,000.What is the total cost? $__________ If the average cost is the total cost divided by the number of books printed, find the average cost of producing 10,000 textbooks. $__________ Find the cost to produce one more textbook when you have already produced 10,000 textbooks. $__________

Question 49

Find the equation of the line with x -intercept 9 and y -intercept 2.

Question 50

To produce this textbook, suppose the publisher spent $165,000 for typesetting and $8.50 per book for printing and binding. The total cost to produce and print n books can be written as Total cost to produce n textbooks = Fixed cost + Variable cost = If the average cost is the total cost divided by the number of books printed, find the average cost of producing 10,000 textbooks.

A) $25
B) $23
C) $19
D) $140
E) $17

Question 51

In an aerobics class, the instructor indicates that her students' exercise heart rate is 15% of their maximum heart rate, where maximum heart rate is 220 minus their age. Determine the equation that gives exercise heart rate E in terms of age A .

Question 52

Write the equation of the line with the slope m = - 4 and y -intercept b = - 2.

Question 53

For the following relation, give the domain and range and indicate whether it is a function. {(4, 1), (5, 6), (2, 4)}

A) Domain = {4, 5, 2}; Range = {1, 6, 4}; a function
B) Domain = {1, 6, 4}; Range = {4, 5, 2}; not a function
C) Domain = {4, 5, 2}; Range = {1, 6, 4}; not a function
D) Domain = {6, 5, 2}; Range = {5, 6, 4}; a function
E) Domain = {5, 6, 4}; Range = {6, 5, 2}; not a function

Question 54

Find the equation of the line parallel to the graph of 7 x - y = 9 that contains the point (- 1, 5).

Question 55

Find the equation of the line that passes through the pair of points. Write your answer in standard form.

Question 56

Write the equation of the line with the slope m = 4 and y -intercept b = 6.

Question 57

Line l is perpendicular to the graph of the equation - 2 x - 5 y = 4 and contains the point (9, - 7). Find the equation for l .

Question 58

Write the equation of the line with the slope and y -intercept .

Question 59

Find the equation of the line with x -intercept 9 and y -intercept 2.

A)
B)
C)
D)
E)

Question 60

Line l is perpendicular to the graph of the equation - 2 x - 7 y = 8 and contains the point (3, - 2). Find the equation for l .

A)
B)
C)
D)
E)

Question 61

Hali is tossing a quarter into the air with an underhand motion. The distance the quarter is above her hand at any time is given by the function where h is the height of the quarter in feet, and t is the time in seconds. Use the data from the table to graph the function. TIME (SEC) FUNCTION RULE DISTANCE (FT) t h 0 0 0.1 1.08 0.2 1.92 0.3 2.52 0.4 2.88 0.5 3 0.6 2.88 0.7 2.52 0.8 1.92 0.9 1.08 1 0

A)
B)
C)
D)

Question 62

A rectangle is 6 inches longer than it is wide. Let x = the width, P = the perimeter and A = the area of the rectangle. Write an equation that will give the perimeter P in terms of the width x of the rectangle.

A)
B)
C)
D)
E)

Question 63

A ball is thrown straight up into the air from ground level. The relationship between the height h of the ball at any time t is illustrated by the following graph: The horizontal axis represents time t , and the vertical axis represents height h . State the domain and the range.

A)
B)
C)
D)
E)

Question 64

The following graph shows the relationship between a company s profits P and the number of items it sells x . ( P is in dollars.) What is their maximum profit?

A) Their maximum profit is $250.
B) Their maximum profit is $200.
C) Their maximum profit is $325.
D) Their maximum profit is $800.
E) Their maximum profit is $400.

Question 65

Hali is tossing a quarter into the air with an underhand motion. The distance the quarter is above her hand at any time is given by the function where h is the height of the quarter in feet, and t is the time in seconds. Fill in the table.

A)
B)
C)
D)

Question 66

Does the graph represent a function?

A) no
B) yes

Question 67

Does the graph represent a function?

A) yes
B) no

Question 68

Suppose you have a job that pays $7.25 and hour and you work anywhere from 15 and 31 hours per week. Write an equation, with a restriction on the variable that gives the amount of money you will earn for working hours in one week.

A)
B)
C)
D)
E)

Question 69

The formula for the area of a circle with radius is given by The formula shows that is a function of State the domain and the range of the function

A)
B)
C)
D)
E)

Question 70

A rectangle is 4 inches longer than it is wide. Let x = the width, P = the perimeter and A = the area of the rectangle. Write an equation that will give the perimeter P in terms of the width x of the rectangle.

Question 71

Does the graph represent a function?

A) yes
B) no

Question 72

The following graph shows the relationship between a company s profits P and the number of items it sells x . ( P is in dollars.) How many items must the company sell to make their maximum profit?

A) The company must sell 20 items to make their maximum profit.
B) The company must sell 50 items to make their maximum profit.
C) The company must sell 80 items to make their maximum profit.
D) The company must sell 100 items to make their maximum profit.
E) The company must sell 70 items to make their maximum profit.

Question 73

The following graph shows the relationship between a company s profits P and the number of items it sells x . ( P is in dollars.) How many items must the company sell to make their maximum profit? __________ items

Question 74

The following graph shows the relationship between a company s profits P and the number of items it sells x . ( P is in dollars.) State the domain and the range of the function.

A)
B)
C)
D)
E)

Question 75

For the following relation, give the domain and range and indicate whether it is a function. {(4, - 5), (- 1, 7), (4, 2)}

A) Domain = {5, - 1}; Range = {- 1, 7, 2}; a function
B) Domain = {- 1, 7, 2}; Range = {5, - 1}; not a function
C) Domain = {4, - 1}; Range = {- 5, 7, 2}; a function
D) Domain = {4, - 1}; Range = {- 5, 7, 2}; not a function
E) Domain = {- 5, 7, 2}; Range = {4, - 1}; a function

Question 76

State whether the following graph represents a function. The graph __________.

Question 77

The following graph shows the relationship between a company s profits P and the number of items it sells x . ( P is in dollars.) What is their maximum profit? $__________

Question 78

Graph the following relation. Use the graph to find the domain and range, and indicate whether the graph is the graph of a function.

A)
B)
C)
D)

Question 79

Graph the following relation. Use the graph to find the domain and range, and indicate whether the graph is the graph of a function.

A)
B)
C)
D)

Question 80

Graph the following relation. Use the graph to find the domain and range, and indicate whether the graph is the graph of a function.

A)
B)
C)
D)