Question 1

Given the points $$A(2, 5)$$ and $$B(-1, -2)$$, what is the slope of the line passing through these points?

Accepted Answer

$$m = \dfrac{5 - (-2)}{2 - (-1)} = \dfrac{7}{3}$$

Question 2

Which of the following equations represents a vertical line passing through $$x = -4$$?

Accepted Answer

$$x = -4$$

Question 3

A line passes through the point $$(3, 2)$$ and has a slope of $$\dfrac{3}{4}. $$Which of the following is the equation of the line in point-slope form?

Accepted Answer

$$y - 2 = \dfrac{3}{4}(x - 3)$$

Question 4

Which of the following best describes the line with equation $$y = 2$$?

Accepted Answer

A horizontal line with $$y-$$intercept $$2$$

Question 5

Find the equation of the line in slope-intercept form that passes through $$(1, 2)$$ and $$(5, -3).$$

Accepted Answer

$$y = -\dfrac{5}{4}x + \dfrac{13}{4}$$

Question 6

If a line has the equation $$3x + 6y = 12$$, what is its slope and $$y-$$intercept?

Accepted Answer

Slope $$m = -\dfrac{1}{2}$$, $$y-$$intercept $$b = 2$$

Question 7

Which of the following lines is perpendicular to the line $$y = 2x + 1$$?

Accepted Answer

$$y = -\dfrac{1}{2}x + 3$$

Question 8

A real-world scenario: A company’s profit $$P (in $$thousands of dollars) is modeled by the equation $$P = 3x + 12$$, where $$x is $$the number of units sold (in hundreds). What does the slope represent in this context?

Accepted Answer

For every 100 units sold, profit increases by $$3,000$$

Question 9

Given the equation $$2x + 4y = 8$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$4$$, $$y-$$intercept: $$2$$

Question 10

Which of the following statements is true about the slopes of parallel lines?

Accepted Answer

Parallel lines have equal slopes.

Question 11

If the slope of a line is undefined, which of the following best describes the line?

Accepted Answer

A vertical line

Question 12

Which of the following is the general form of a line?

Accepted Answer

$$Ax + By = C$$

Question 13

A line passes through $$(2, 3)$$ and is parallel to the line $$y = -\dfrac{1}{2}x + 4. $$What is the equation of the line in slope-intercept form?

Accepted Answer

Question 14

Which of the following is the correct interpretation of the slope $$m in $$the equation $$y = mx + b$$?

Accepted Answer

The rate of change of $$y$$ with respect to $$x$$

Question 15

If a line has the equation $$y - 2 = 4(x - 1)$$, what is its slope and a point it passes through?

Accepted Answer

Slope $$m = 4$$, passes through $$(1, 2)$$

Question 16

Which of the following lines is perpendicular to $$y = \dfrac{1}{3}x - 2$$?

Accepted Answer

$$y = -3x + 1$$

Question 17

A horizontal line passes through the point $$(-2, 5). $$What is its equation?

Accepted Answer

$$y = 5$$

Question 18

Given the line $$y = 2x + 3$$, what is the $$y-$$coordinate when $$x = -1$$?

Accepted Answer

$$y = 1$$

Study Guide: Lines and Their Equations in Precalculus

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