Deck 3: Section 1: Linear Equations and Inequalities in Two Variables

Question 1

The budget deficit for the city of Gotham can be modeled by the equation D = 1.2n + 13.5
Where n is the number of years since 1990 and D is the deficit in millions of dollars. Which answer below correctly displays the graph of the equation?

A)

B)

C)

D)

Answer 1

Question 2

Write the equation in standard form using only integers and a positive coefficient for x.

A) x - 3y = 6
B) -x + 3y = -6
C) x + 3y = 6
D) x - 3y = 2

Answer 2

x - 3y = 6

Question 3

Which of the following is the correct graph of the line through (3, 2) with slope ?

A)

B)

C)

D)

Answer 3

Question 4

Which point below is located at coordinates (-1, 3)?

A) K
B) G
C) M
D) A

Question 5

Line l goes through (3, 2) and is parallel to the line through (4, 1) and (-3, 3). Find the slope of l.

A) Undefined
B)
C) 3
D)

Question 6

Which figure below is the correct graph of the linear equation x = 3?

A)

B)

C)

D)

Question 7

Gotham City's budget deficit was $6.2 million in 1993 and $2.4 million in 1998. Find the slope of the line through (1993, 6.2) and (1998, 2.4) and interpret your result.

A) -0.760 slope; the slope of the deficit is decreasing by $0.760 million per year
B) -0.760 slope; the deficit is increasing by $0.760 million per year
C) -0.760 slope; the deficit is decreasing by $0.760 million per year
D) -0.760 slope; the deficit decreased by $0.760 million during the period between 1993 and 1998.

Question 8

The price of a 2-hour plumbing repair job is $130 and the price of a 5-hour job is $250. Write an equation for the cost C of a t-hour repair job and use the equation to find the cost of a repair job lasting 7 hours.

A) C = 40t + 50; $330
B) C = 40t; $280
C) C = 40t + 40; $320
D) C = 50t + 40; $390

Question 9

A playground equipment manufacturer plans to spend $300,000 on a new facility plus $160 for each swing set made.The formula C = 160n + 300,000 gives the cost in dollars to manufacture n swing sets. What is the marginal cost of the nth swing set? [Hint - the marginal cost of the nth swing set is the difference in cost of producing n + 1 swing sets and n swing sets).

A) $170
B) $160
C) $300,000
D) $320

Question 10

Complete the ordered pair so that it satisfies the given equation. y = 7x - 13: (4, ___)

A) (4, 16)
B) (4, 28)
C) (4, 15)
D) (4, 41)

Question 11

Write an equation in slope-intercept form for a line l that goes through (9, -1) and has a slope of .

A)
B)
C)
D)

Question 12

Find the slope of the line that contains the points (8,6) and (-5,1).

A)
B) 13
C)
D) 5

Question 13

Write a formula that expresses the relationship described below. Use k as a constant of variation. u varies directly as v

A)
B) u = kv
C) u = k + v
D) k = uv

Question 14

Find the x- and y-intercepts of 4x + 3y = -12 and use them to graph the equation.

A)

B)

C)

D)

Question 15

Which figure below is the correct graph of the linear equation y = -2x - 1?

A)

B)

C)

D)

Question 16

Line l goes throught the point (5,-2) and is perpendicular to the line through (-2, 1) and (-4, -2). Find the equation (in slope-intercept form) for l.

A)
B)
C)
D)

Question 17

Find the slope and the y-intercept of the line represented by 6x + 7y = -12.

A) slope
and y-intercept

B) slope
and y-intercept

C) slope
and y-intercept

D) slope
and y-intercept

Question 18

Find the equation (in standard form) of the line through (2, -5) and (4, -6).

A)
B)
C)
D)

Question 19

Determine the slope of the line graphed below.

A)
B) Undefined
C)
D) -3

Question 20

Which of the following is the correct graph of the equation y = 3x - 1?

A)

B)

C)

D)

Question 21

Does the point (2, 14) satisfy the inequality y $\le$ 2x - 2?

Question 22

The time to drive from Gotham City to Farmville varies inversely with the average speed. If the drive takes 6.2 hours at 42 mph, then how long will it take at 63 mph? Round to the nearest tenth of an hour.

A) 4.1 hours
B) 3.5 hours
C) 3.2 hours
D) 3.7 hours

Question 23

If s varies inversely as x and s = 4 when x = -4, then find s when x = 2.

A) -8
B) 4
C) -16
D) -2

Question 24

Which graph below correctly indicates the solution set of the linear inequality ?

A)

B)

C)

D)

Question 25

Tim works at a bakery and can prepare a birthday cake in 4 hours. It takes him 5 hours to prepare a wedding cake. If Tim works a 40-hour week, which graph below correctly illustrates the number of each type of cake Tim can bake per week?

A)

B)

C)

D)

Question 26

Write a formula that expresses the relationship described below. P varies jointly as x and y and P = 4 when x = 7 and y = -7

A)
B)
C)
D)