Question 1

A city engineer is designing a wheelchair ramp that rises 2 feet for every 12 feet of horizontal distance. What is the slope of the ramp?

Accepted Answer

$$m = \frac{2}{12}$$

Question 2

Given two points on a line, $$(1, -3)$$ and $$(4, 3)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = \frac{3 - (-3)}{4 - 1} = \frac{6}{3} = 2$$

Question 3

Which of the following equations represents a line with a slope of zero?

Accepted Answer

$$y = 5$$

Question 4

A vertical line passes through the point $$(3, -2). $$What is its equation?

Accepted Answer

$$x = 3$$

Question 5

A line passes through $$(0, -3)$$ and has a slope of $$1. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = x - 3$$

Question 6

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

Accepted Answer

$$m = 0$$

Question 7

A biologist tracks the population of a species over time. If the population increases by 50 every year, and the initial population is 200, which equation models the population $$P$$ after $$t$$ years?

Accepted Answer

$$P = 50t + 200$$

Question 8

Given the equation $$y = -2x - 3$$, what is the y-intercept and slope?

Accepted Answer

y-intercept: $$-3$$, slope: $$-2$$

Question 9

A line passes through $$(2, 4)$$ and $$(2, -1). $$What is the slope of this line?

Accepted Answer

$$m = 	ext{undefined}$$

Question 10

Which graph below represents the equation $$x = 3$$?

Accepted Answer

A vertical line crossing $$x = 3$$

Question 11

Write the point-slope form of the equation for a line with slope $$\frac{2}{3}$$ passing through $$(1, 3).$$

Accepted Answer

$$y - 3 = \frac{2}{3}(x - 1)$$

Question 12

A line has the equation $$y = mx + b. If$$ $$m is $$negative, which direction does the line go as you move from left to right?

Accepted Answer

Down

Question 13

A line passes through $$(2, -4)$$ and has a slope of $$0. $$What is its equation in point-slope form?

Accepted Answer

$$y + 4 = 0(x - 2)$$

Question 14

Which of the following is the correct slope-intercept form for a line with slope $$\frac{2}{3}$$ and y-intercept $$1$$?

Accepted Answer

$$y = \frac{2}{3}x + 1$$

Question 15

A horizontal line passes through $$(2, -4). $$What is its equation?

Accepted Answer

$$y = -4$$

Question 16

If a line has a slope of $$0$$ and passes through $$(3, -2)$$, which of the following is true?

Accepted Answer

The line is horizontal and its equation is $$y = -2$$

Question 17

A line passes through $$(1, 2)$$ and $$(4, 2). $$What is the slope of this line?

Accepted Answer

$$m = 0$$

Question 18

Which of the following is NOT a possible value for the slope of a line?

Accepted Answer

$$m = \infty$$

Question 19

A line has the equation $$y = mx + b. If$$ $$m = 0$$, what does the graph look like?

Accepted Answer

A horizontal line crossing the y-axis at $$b$$

Question 20

Which of the following is the correct point-slope form for a line with slope $$-2$$ passing through $$(0, 5)$$?

Accepted Answer

$$y - 5 = -2(x - 0)$$

Slopes and Equations of Lines: Study Notes for College Algebra

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