Question 1

Given the line $$y = 3x + 2$$, which of the following is the equation of a line parallel to it that passes through the point $$(1, 4)$$?

Accepted Answer

Question 2

Which of the following statements is TRUE about the slopes of perpendicular lines?

Accepted Answer

Perpendicular lines have slopes that are negative reciprocals.

Question 3

A horizontal line passes through $$(2, 5). $$Which equation represents a line perpendicular to it?

Accepted Answer

$$x = 2$$

Question 4

If a line has slope $$m = 4$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$-\frac{1}{4}$$

Question 5

Which of the following is the point-slope form of the equation for a line passing through $$(3, -2)$$ and parallel to $$y = -5x + 7$$?

Accepted Answer

$$y + 2 = -5(x - 3)$$

Question 6

A line passes through $$(0, 0)$$ and is perpendicular to the line $$y = \frac{1}{2}x + 4. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -2x$$

Question 7

Which of the following is the general form of the equation for a line passing through $$(1, 2)$$ and parallel to $$y = 4x - 3$$?

Accepted Answer

$$4x - y - 2 = 0$$

Question 8

If two lines are both vertical, what can be said about their slopes and their relationship?

Accepted Answer

Their slopes are undefined and they are parallel.

Question 9

A line passes through $$(2, -1)$$ and is perpendicular to $$y = 2x + 5. $$What is its equation in slope-intercept form?

Accepted Answer

Question 10

Which of the following is the correct slope for a line perpendicular to $$y = -\frac{3}{4}x + 2$$?

Accepted Answer

$$\frac{4}{3}$$

Question 11

A city street runs along the line $$y = 2x + 1. A $$new cross street must be perpendicular and pass through $$(3, 7). $$What is the equation of the cross street in point-slope form?

Accepted Answer

$$y - 7 = -\frac{1}{2}(x - 3)$$

Question 12

Which of the following is the slope-intercept form of a line passing through $$(4, 5)$$ and parallel to $$y = -2x + 1$$?

Accepted Answer

$$y = -2x + 13$$

Question 13

A vertical line passes through $$(6, -2). $$Which equation represents a line perpendicular to it?

Accepted Answer

$$y = -2$$

Question 14

If the product of the slopes of two lines is $$-1$$, what is their relationship?

Accepted Answer

They are perpendicular.

Question 15

A line passes through $$(0, 3)$$ and is parallel to $$y = \frac{1}{3}x - 2. $$What is its equation in slope-intercept form?

Accepted Answer

Question 16

Which of the following is the general form of the equation for a line passing through $$(2, 1)$$ and perpendicular to $$y = 5x - 4$$?

Accepted Answer

$$x + 5y - 7 = 0$$

Question 17

A line passes through $$(1, -3)$$ and is perpendicular to $$y = 0. $$What is its equation?

Accepted Answer

$$x = 1$$

Question 18

Which of the following is the correct slope for a line parallel to $$y = -\frac{2}{5}x + 7$$?

Accepted Answer

$$-\frac{2}{5}$$

Question 19

A medical researcher plots the line $$y = 0.75x + 2 to $$represent a dosage-response curve. If a new drug's response curve must be perpendicular and pass through $$(4, 5)$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = -\frac{4}{3}x + \frac{23}{3}$$

Equations of Parallel and Perpendicular Lines

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