Question 1

Given two points $$A(2, 3)$$ and $$B(5, 11)$$, what is the slope $$m of $$the line passing through these points?

Accepted Answer

$$m = \dfrac{11 - 3}{5 - 2} = \dfrac{8}{3}$$

Question 2

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

Accepted Answer

The slope is undefined because division by zero occurs.

Question 3

A line passes through the point $$(1, -2)$$ and has a slope of $$4. $$What is the equation of the line in point-slope form?

Accepted Answer

$$y + 2 = 4(x - 1)$$

Question 4

Which of the following equations represents a horizontal line passing through the point $$(0, 5)$$?

Accepted Answer

$$y = 5$$

Question 5

If a line has the equation $$y = -\dfrac{2}{3}x + 7$$, what is its slope and $$y-$$intercept?

Accepted Answer

Slope: $$-\dfrac{2}{3}$$, $$y-$$intercept: $$7$$

Question 6

Which of the following lines is parallel to $$y = 3x - 2$$?

Accepted Answer

$$y = 3x + 5$$

Question 7

Find the equation of the line perpendicular to $$y = 2x + 1$$ and passing through the point $$(4, -3). $$Write your answer in slope-intercept form.

Accepted Answer

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

Question 8

Given the general form $$2x - 3y = 6$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$3$$, $$y-$$intercept: $$-2$$

Question 9

If the rise between two points on a line is $$5$$ and the run is $$-2$$, what is the slope of the line?

Accepted Answer

$$m = -2.5$$

Question 10

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

Accepted Answer

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

Question 11

A road rises $$8$$ meters for every $$200$$ meters of horizontal distance. What is the slope of the road?

Accepted Answer

$$m = \dfrac{8}{200} = 0.04$$

Question 12

Which equation is in slope-intercept form?

Accepted Answer

$$y = mx + b$$

Question 13

If a line passes through $$(0, 0)$$ and $$(4, 6)$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = \dfrac{3}{2}x$$

Question 14

Which of the following best describes the effect on the steepness of a line if the rise stays the same but the run decreases?

Accepted Answer

The line becomes steeper.

Question 15

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

Accepted Answer

$$x = 5$$

Question 16

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

Accepted Answer

$$Ax + By = C$$

Question 17

If two lines have slopes $$m_1 = 2$ and m_2$ = -\dfrac{1}{2}$$, what is the relationship between the lines?

Accepted Answer

They are perpendicular.

Question 18

A line has the equation $$y = 0. $$Which of the following statements is true?

Accepted Answer

It is a horizontal line passing through the $$x-$$axis.

Question 19

Which of the following is the correct interpretation of the slope in the context of a real-world scenario, such as a ramp?

Accepted Answer

The slope represents the ratio of vertical rise to horizontal run.

Lines and Their Equations: Slope, Forms, and Graphs

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