Deck 2: Linear Equations in Two Variables and Functions

Question 1

Find the x-intercept and the y-intercept then graph the equation.

Answer 1

B

Question 2

Find the x-intercept and the y-intercept then graph the equation.

Answer 2

A

Question 3

Find the x-intercept and the y-intercept and graph both. Then graph the line.

Answer 3

A

Question 4

A manufacturing company produces plastic pipe used in wastewater treatment applications. The pipe measures 4 inches in diameter and is cut to 10-foot lengths. The manufacturers fixed costs are
$8000 per month (The fixed cost is the cost to operate the company even if it produces no pipe. It
Includes rent, debt payments, salaries, etc.). It costs an additional $1.45 for each unit of pipe produced.
The overall monthly production costs are described by the linear equation where y represents the total monthly operating cost and x represents the number of units of pipe
Produced.
What does the y-intercept mean in the context of this problem?

A) The y-intercept represents the cost ($1.45) per unit of pipe.
B) The y-intercept indicates that the fixed cost increases by $8000 per month.
C) The y-intercept represents the increase in total cost when production is increased by one unit of pipe.
D) The y-intercept represents the fixed cost of $8000.

Question 5

Write the word or phrase that best completes each statement or answers the question.
A business owner buys several new computers for the office for $1750 each. The accounting office
depreciates each computer by $250 per year. The value y (in $) for each computer can be
represented by y = 1750  250x, where x is the number of years after purchase.
Computer Value Versus Years After Purchase a. How much will a computer be worth 1 yr after purchase?
b. After how many years will the computer be worth only $250?
c. Determine the y-intercept and interpret its meaning in the context of this problem.
d. Determine the x-intercept and interpret its meaning in the context of this problem.

Question 6

Determine if the ordered pair is a solution to the linear equation.

A) No
B) Yes

Question 7

Graph the linear equation.

Question 8

Graph the linear equation.

Question 9

Find the x-intercept and the y-intercept and graph both. Then graph the line.

Question 10

Determine if the ordered pair is a solution to the linear equation.

A) No
B) Yes

Question 11

Plot the point on the rectangular coordinate system.

Question 12

Determine if the ordered pair is a solution to the linear equation. 4x + 3y = -13; (2, -7)

A) Yes
B) No

Question 13

Find the x-intercept and the y-intercept then graph the equation.

Question 14

Plot the point on the rectangular coordinate system.

Question 15

Give the coordinates of the specified point.

A) (-3,0)
B) (3,0)
C) (0,-3)
D) (0,3)

Question 16

Write the word or phrase that best completes each statement or answers the question.
Complete the table. Then graph the line defined by the points.

Question 17

Plot the point on the rectangular coordinate system. (2, -4)

Question 18

Graph the linear equation.

Question 19

Determine if the ordered pair is a solution to the linear equation. 2x + 7y = 14; (6, 0)

A) Yes
B) No

Question 20

Graph the linear equation.

Question 21

Question 22

The slope of a line is given. Find the slope of a line parallel to the given line and perpendicular to the given line.

Question 23

Use the slope formula to determine the slope of the line containing the two points. (-4, -5) and (-8, -5)

Question 24

If a plane loses 1200 feet in altitude over a horizontal distance of 9000 feet, what is the slope?

Question 25

Use the slope formula to determine the slope of the line containing the two points. Round tothe nearest hundredth.
(-0)5, -1.9) and (-2.9, -5.2)

A) 0.73
B) 1.38
C) 2.09
D) 1.64

Question 26

Identify the line as either vertical or horizontal, and graph the line.

Question 27

Use the slope formula to determine the slope of the line containing the two points. (4, -8) and (-1, -2)

Question 28

Use the slope formula to determine the slope of the line containing the two points. (3, 0) and (0, -5)

Question 29

Identify the line as either vertical or horizontal, and graph the line.

Question 30

Estimate the slope of the line from its graph.

Question 31

A metal mast is stabilized with 3 guy wires (see figure). Find the slope of one of the guy wires if d = 100 feet and h = 70 ft.

Question 32

Use the slope formula to determine the slope of the line containing the two points.

Question 33

Question 34

Question 35

Question 36

The graph shows the enrollment at Riverside Community College for selected years. Use the coordinates of the given points to find the slope of the line. Interpret the meaning of the slope in the context of this problem

A) m = 300; Enrollment increases by approximately 300 students per year.
B) m = 150; Enrollment increases by an approximate factor of 150 students per year.
C) m = 300; Enrollment increases by an approximate factor of 300 students per year.
D) m = 150; Enrollment increases by approximately 150 students per year.

Question 37

Use the slope formula to determine the slope of the line containing the two points. (9, 5) and (9, 8)

Question 38

Find the slope of the hill.

Question 39

The slope of a line is given. Find the slope of a line parallel to the given line and perpendicular to the given line.

Question 40

Which of the lines defined here have only one unique intercept? a. x = 8
B) -8x - 7y = -7
C) 9y = 5
D) -3x - 3y = 0

A) b.
B) b. and d.
C) a. and c.
D) a., c., and d.

Question 41

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.

Question 42

Match the equation with the correct graph below.

Question 43

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.

Question 44

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.

Question 45

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) neither
B) perpendicular
C) parallel

Question 46

Determine the slope and the y-intercept of the line. 63 = -9y

A) Slope: 0; y-intercept: (0, -7)
B) Slope: undefined; y-intercept: (-7, 0)
C) Slope: 0; y-intercept: (-7, 0)
D) Slope: 1; y-intercept: (0, -7)

Question 47

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) neither
B) perpendicular
C) parallel

Question 48

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) parallel
B) neither
C) perpendicular

Question 49

Determine the slope and the y-intercept of the line.

Question 50

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.

Question 51

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) parallel
B) neither
C) perpendicular

Question 52

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.
The line passes through the point (-4, -20) and has a slope of 3.

Question 53

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) parallel
B) perpendicular
C) neither

Question 54

Match the equation with the correct graph below.

Question 55

Write the equation in slope-intercept form. Then graph the line using the slope and y-intercept.

Question 56

Determine the slope and the y-intercept of the line. Round your answer to three decimalplace, if necessary.
Y = 1.6x - 11.5

A) Slope: 1.6; y-intercept: (0, 11.5)
B) Slope: 1.6; y-intercept: (0, -11.5)
C) Slope: 0.625; y-intercept: (0, -11.5)
D) Slope: 11.5; y-intercept: (0, 1.6)

Question 57

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) parallel
B) neither
C) perpendicular

Question 58

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) parallel
B) perpendicular
C) neither

Question 59

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) neither
B) parallel
C) perpendicular

Question 60

Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.

A) perpendicular
B) neither
C) parallel

Question 61

Write an equation of the line satisfying the given conditions. The line passes through (2, 9) and has a zero slope.

A) x = 2
B) y = 2
C) x = 9
D) y = 9

Question 62

Write the word or phrase that best completes each statement or answers the question.
The figure represents the average credit card debt for selected households in Silerville. Let y represent the credit card debt in dollars. Let x represent the year, where x = 0 corresponds to
the year 1990, x = 4 represents 1994, and so on.
a. Use the ordered pairs given in the graph, (0, 3299) and (16, 7415) to find a linear equation to estimate the
average credit card debt versus the year. Round the slope to the nearest tenth.
b. Use the model from (a) to estimate the average debt in 2003. Round to the nearest dollar.
c. Interpret the slope of the model in the context of this problem.

Question 63

A tool rental store charges a flat fee of $9.50 to rent a chain saw, and $3.75 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days.

A) y = 9.50x + 3.75
B) y = 3.75x - 9.50
C) y = 3.75(x + 9.50)
D) y = 3.75x + 9.50

Question 64

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form.

Question 65

The S-Cargo shipping company calculates shipping charges using the linear model y = 2.72x,
Where y is the cost in dollars and x is the weight of the package in pounds . Use the linear
Model to compute weight of a package with a shipping cost of $21.76. Round to the nearest
Hundredth of a pound, if necessary.

A) 2.94 lb
B) 21.76 lb
C) 10.72 lb
D) 8.00 lb

Question 66

The following figure represents the average hourly wage for employees of MegaMart from 1980 to 2005. Let y represent the hourly wage and let x represent the year, where x = 0 corresponds to the year 1980,
X = 1 represents 1981, and so on. Then the average wage can be approximated by the equation
Y = 0.17x + 3.02, where Use the linear equation to approximate the average wage for the year 1985 and compare it to the actual
Wage of $3.75 per hour.

A) $4.72 per hour; the calculated wage was $0.97 more than the actual wage.
B) $3.02 per hour; the calculated wage was $0.73 less than the actual wage.
C) $3.02 per hour; the calculated wage was $0.17 more than the actual wage.
D) $3.87 per hour; the calculated wage was $0.12 more than the actual wage.

Question 67

Write an equation of the line satisfying the given conditions. The line is perpendicular to the x-axis and passes through (-4, 8).

A) x = -4
B) y = -4
C) y = 8
D) x = 8

Question 68

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.

Question 69

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form.

Question 70

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form.

Question 71

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form.
The line is perpendicular to the line defined by y = 4x - 8 and passes through the point(8, 3).

Question 72

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.

Question 73

A tool rental store charges a flat fee of $4.00 to rent a chain saw, and $5.25 for each day, including the first. Use a linear equation to find the cost of renting the saw for one week.

A) $9.25
B) $40.75
C) $36.75
D) $35.50

Question 74

Write an equation of the line satisfying the given conditions. The line passes through (-9, -6) and has an undefined slope.

A) y = -9
B) x = -9
C) y = -6
D) x = -6

Question 75

Write an equation of the given line in slope-intercept form.

Question 76

Write an equation of the line satisfying the given conditions. The line passes through (-6, -9) and (-6, -11).

A) x = -6
B) y = -6x
C) y = 6
D) y = -6

Question 77

Write an equation of the line satisfying the given conditions. Write the answer inslope-intercept form.

Question 78

A tool rental store charges a flat fee of $7.00 to rent a chain saw, and $6.75 for each day, including the first. If you need to rent the saw and absolutely refuse to spend more than $74.50, what's the
Maximum number of days you can keep the saw?

A) 14 days
B) 10 days
C) 5 days
D) 7 days

Question 79

Write an equation of the line satisfying the given conditions. The line is parallel to the x-axis and passes through (9, 4)

A) x = 4
B) y = 4
C) y = 9
D) x = 9

Question 80

The S-Cargo shipping company calculates shipping charges using the linear model y = 2.71x,
Where y is the cost in dollars and x is the weight of the package in pounds . Use the linear
Model to compute the shipping cost for a package weighing 2 lb. Round to the nearest cent.

A) $0.74
B) $5.42
C) $2.00
D) $4.71