Question 1

Given two points $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$, what is the formula for the slope $$m of $$the line passing through these points?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 2

If a line has a slope of $$0$$, what is the orientation of the line?

Accepted Answer

Horizontal

Question 3

What is the equation of a vertical line passing through the point $$(3, -2)$$?

Accepted Answer

$$x = 3$$

Question 4

Which of the following best describes the slope of a vertical line?

Accepted Answer

Undefined

Question 5

If the slope of a line is $$-4$$, which direction does the line slant from left to right?

Accepted Answer

Downward

Question 6

What is the point-slope form of the equation of a line with slope $$m$$ passing through the point $$(x_1$, y_1$)$$?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 7

A line passes through the points $$(2, 5)$$ and $$(4, 9). $$What is its slope?

Accepted Answer

$$m = 2$$

Question 8

What is the slope-intercept form of a line with slope $$-3$$ and y-intercept $$7$$?

Accepted Answer

$$y = -3x + 7$$

Question 9

Given the equation $$2x + 5y = 10$$, what is the y-intercept?

Accepted Answer

$$y = 2$$

Question 10

If two lines are parallel, what must be true about their slopes?

Accepted Answer

Their slopes are equal

Question 11

What is the slope of a line perpendicular to a line with slope $$\frac{1}{3}$$?

Accepted Answer

$$-3$$

Question 12

A line passes through $$(1, 2)$$ and $$(3, 8). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 3x - 1$$

Question 13

Which of the following equations represents a horizontal line?

Accepted Answer

$$y = 4$$

Question 14

If the equation of a line is $$y = 5x + 2$$, what is the average rate of change of $$y$$ with respect to $$x$$?

Accepted Answer

$$5$$

Question 15

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

Accepted Answer

$$Ax + By = C$$

Question 16

A line has equation $$y = -2x + 5. $$What is the slope and y-intercept?

Accepted Answer

Slope $$-2$$, y-intercept $$5$$

Question 17

If the slope of a line increases, what happens to the steepness of the line?

Accepted Answer

The line becomes steeper

Question 18

Which of the following statements is true about perpendicular lines?

Accepted Answer

The product of their slopes is $$-1$$

Question 19

A line passes through $$(0, 3)$$ and is parallel to the line $$y = 2x + 1. $$What is its equation?

Accepted Answer

$$y = 2x + 3$$

Question 20

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

Accepted Answer

$$y = -2x + 8$$

Lines and Their Equations: Slope, Forms, and Relationships

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