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

Study Guide - Practice Questions

Study Guide - Flashcards