Question 1

Given the points (2, 5) and (6, 13), what is the slope of the line passing through these points?

Accepted Answer

$$m = \frac{13 - 5}{6 - 2} = 2$$

Question 2

Which of the following equations represents a line with an undefined slope?

Accepted Answer

$$x = 4$$

Question 3

A city charges a base fee of $$20 for water service plus 1.50 $$per 100 gallons used. Which equation models the total cost $$y$$ for $$x$$ hundred gallons of water?

Accepted Answer

$$y = 1.5x + 20$$

Question 4

Find the slope of the line given by the equation $$4x - 2y = 8.$$

Accepted Answer

$$m = 2$$

Question 5

Which of the following best describes the slope of a horizontal line?

Accepted Answer

$$m = 0$$

Question 6

If a line has the equation $$y = -\frac{1}{3}x + 7$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$m = 3$$

Question 7

Which of the following pairs of lines are parallel?

Accepted Answer

$$y = 2x + 5$$ \ y = 2x - 3$

Question 8

A line passes through the points (−1, 4) and (3, −8). What is the slope of the line?

Accepted Answer

$$m = \frac{-8 - 4}{3 - (-1)} = \frac{-12}{4} = -3$$

Question 9

The price of a concert ticket increases by $$2.50 each year after 2010, when the price was 40. $$Write the equation for the ticket price $$y in $$year $$x ($$where $$x is $$the number of years since 2010), and find the price in 2020.

Accepted Answer

$$y = 2.5x + 40$$, so in 2020 ($$x = 10$$), $$y = 2.5(10) + 40 = 65$$

Question 10

Which of the following statements is true about the slopes of perpendicular lines (not vertical or horizontal)?

Accepted Answer

Their slopes are negative reciprocals of each other.

Question 11

Given the equation $$-2y = 8x - 10$$, what is the slope of the line?

Accepted Answer

$$m = -4$$

Question 12

A road rises 15 meters for every 200 meters of horizontal distance. What is the slope of the road?

Accepted Answer

$$m = \frac{15}{200} = 0.075$$

Question 13

Which line is perpendicular to $$y = 5x + 2$$?

Accepted Answer

$$y = -\frac{1}{5}x + 7$$

Question 14

If two lines are parallel and neither is vertical, what must be true about their slopes?

Accepted Answer

Their slopes are equal.

Question 15

A horizontal line passes through the point (7, -3). What is its equation?

Accepted Answer

$$y = -3$$

Question 16

Which of the following best describes the graph of $$y = -2x + 5$$?

Accepted Answer

A line that goes downward to the right

Question 17

Given the points (−2, 7) and (−2, −5), what is the slope of the line passing through them?

Accepted Answer

Undefined

Question 18

If the equation of a line is $$y = 0.5x + 4$$, what is the y-intercept?

Accepted Answer

$$(0, 4)$$

Question 19

A company’s profit $$y (in $$thousands of dollars) is modeled by $$y = 12x - 30$$, where $$x is $$the number of years since 2015. In what year will the company break even (profit is zero)?

Accepted Answer

2017.5

The Slope of a Line: Graphs and Functions in Intermediate Algebra

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