Question 1

Given the points $A(5, 13)$ and $B(20, -6)$, what is the slope of the line passing through these points?

Accepted Answer

$m = \dfrac{-19}{15}$

Question 2

Find the slope of the line passing through the points $(20, -6)$ and $(11, 0)$. Which of the following is correct?

Accepted Answer

$m = \dfrac{0 - (-6)}{11 - 20} = \dfrac{6}{-9} = -\dfrac{2}{3}$

Question 3

A line passes through the points $(13, 20)$ and $(6, 11)$. What is its slope?

Accepted Answer

$m = \dfrac{20 - 11}{13 - 6} = \dfrac{9}{7}$

Question 4

Find the slope of the line given by the equation $5x - 4y = 4$.

Question 5

Find the slope of the line given by $2x - 3y = -9$.

Accepted Answer

$m = \dfrac{2}{-3}$

Question 6

What is the slope of the line $y = 9x + 4$?

Accepted Answer

$m = 9$

Question 7

Find the slope of the line $y = -2x + 4$.

Accepted Answer

$m = -2$

Question 8

A line is perpendicular to $3x - 2y = -2$. What is the slope of the perpendicular line?

Accepted Answer

$m = \dfrac{3}{2}$

Question 9

Which of the following is the slope of a line perpendicular to $8x + 5y = 20$?

Accepted Answer

$m = \dfrac{5}{8}$

Question 10

Write the point-slope form of the equation of the line passing through $(0, 2)$ and parallel to $y = -5x$.

Accepted Answer

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

Question 11

Which is the point-slope form of the equation of the line through $(1, 2)$ and parallel to $y = 5x$?

Accepted Answer

$y - 2 = 5(x - 1)$

Question 12

Given a line with slope $-1$ and $y$-intercept $3$, what is its equation in point-slope form?

Accepted Answer

$y - 3 = -1(x - 0)$

Question 13

A line has slope $\dfrac{1}{2}$ and $y$-intercept $0$. What is its equation in point-slope form?

Accepted Answer

$y - 0 = \dfrac{1}{2}(x - 0)$

Question 14

A city is planning a new road that must be perpendicular to an existing road with equation $y = 2x + 5$. What is the slope of the new road?

Accepted Answer

$m = -\dfrac{1}{2}$

Question 15

A biologist tracks the migration of a bird and finds its path can be modeled by the line passing through $(2, 5)$ and $(8, 17)$. What is the equation of the line in point-slope form?

Accepted Answer

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

Question 16

A chemical reaction's rate is modeled by the line $y = -3x + 7$. If a scientist wants to model a process with a rate perpendicular to this, what should the slope be?

Accepted Answer

$m = \dfrac{1}{3}$

Question 17

A medical researcher finds that the relationship between dosage $x$ and patient response $y$ is linear, passing through $(0, 2)$ and $(4, 10)$. What is the slope of this relationship?

Accepted Answer

$m = 2$

Question 18

A line passes through $(3, 7)$ and is parallel to $y = -4x + 1$. What is its equation in point-slope form?

Accepted Answer

$y - 7 = -4(x - 3)$

Question 19

A business's profit $P$ is modeled by the equation $P = 5x - 12$, where $x$ is the number of units sold. What is the slope, and what does it represent?

Accepted Answer

The slope is $5$, representing the profit increase per unit sold.

Slopes and Equations of Lines: Study Notes for College Algebra

Study Guide - Practice Questions

Study Guide - Flashcards