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 $$5x - 4y = 4.$$

Accepted Answer

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

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