Deck 3: Section 2: Linear Equations and Inequalities in Two Variables

Question 1

Graph the point .

Answer 1

Question 2

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 9 hours.

Answer 2

C = 40t + 50; $410

Question 3

Graph the line through (-1, 3) with slope -2.

Answer 3

Question 4

Find the slope of the line that contains the points (-11,2) and (8,-12).

Question 5

Graph the linear equation .

Question 6

Find the slope and the y-intercept of the line represented by 12x + 7y = 5.

Question 7

Find the equation (in standard form) of the line through (2, 0) and (4, -1).

Question 8

Graph the equation y = -3x + 1.

Question 9

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

Question 10

Find the x- and y-intercepts of x + 3y + 2 = 0 and use these intercepts to graph the equation.

Question 11

Write an equation in slope-intercept form for a line l that goes through (12, -1) and has a slope of .

Question 12

The lines are perpendicular. Find the equation (in slope-intercept form) for the solid line.

Question 13

Gotham City's budget deficit was $4.5 million in 1991 and $4.6 million in 2000. Find the slope of the line through (1991, 4.5) and (2000, 4.6) and interpret your result.

Question 14

Complete the ordered pair so that it satisfies the given equation.
y = -4x + 3: (-10, ___)

Question 15

Determine the slope of the line graphed below. Show your work.

Question 16

Write a formula that expresses the relationship described below. Use k as a constant of variation.
P varies directly with T

Question 17

A playground equipment manufacturer plans to spend $300,000 on a new facility plus $140 for each swing set made.The formula C = 140n + 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).

Question 18

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

Question 19

The budget deficit for Central City can be modeled by the equation
D = 0.5n + 6.5
where n is the number of years since 1990 and D is the deficit in millions of dollars. Graph the equation for n ranging from 0 to 20.

Question 20

Write the equation of the line shown below.

Question 21

Does the point (-4, -1) satisfy the inequality y $\le$ 6x - 5?

Question 22

The time to drive from Gotham City to Farmville varies inversely with the average speed. If the drive takes 5.0 hours at 49 mph, then how long will it take at 70 mph? Round to the nearest tenth of an hour.

Question 23

Write a formula that expresses the relationship described below.
P varies jointly as x and y and P = -8 when x = -2 and y = 7

Question 24

Graph the solution set of the linear inequality ?

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. Tim works a 40-hour week and he must bake at least as many wedding cakes as birthday cakes. Draw a graph that illustrates the number of each type of cake Tim can bake per week.