Question 1

Which of the following is the correct formula for the slope $$m of a $$line passing through the points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

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

Question 2

A line passes through the points $$(2, 5)$$ and $$(5, 11). $$What is the slope of the line?

Accepted Answer

$$m = 2$$

Question 3

Which of the following equations is in standard form for a linear equation?

Accepted Answer

$$2x - 3y = 7$$

Question 4

What is the slope of the line given by the equation $$y = -\frac{4}{3}x + 2$$?

Accepted Answer

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

Question 5

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

Accepted Answer

Undefined

Question 6

A horizontal line passes through the point $$(0, 4). $$What is its equation?

Accepted Answer

$$y = 4$$

Question 7

Find the $$y-$$intercept of the line $$3x + 2y = 8.$$

Accepted Answer

Question 8

Which of the following lines has a negative slope?

Accepted Answer

$$y = -2x + 1$$

Question 9

What is the average rate of change of the function $$f(x)$$ from $$x_1 = -1.5$ to x_2$ = 0 if$$ $$f(-1.5) = 0$$ and $$f(0) = 2$$?

Accepted Answer

$$\frac{2 - 0}{0 - (-1.5)} = \frac{2}{1.5} = \frac{4}{3}$$

Question 10

A line passes through the points $$(-3, 2)$$ and $$(2, -4). $$What is the equation of the line in standard form?

Accepted Answer

$$6x + 5y = -8$$

Question 11

Which of the following best describes the graph of $$x = 2$$?

Accepted Answer

A vertical line passing through $$(2, 0)$$

Question 12

If a line has a slope of $$0$$, which of the following statements is true?

Accepted Answer

The line is horizontal

Question 13

Given the equation $$y = mx + b$$, what does $$b$$ represent?

Accepted Answer

The $$y-$$intercept

Question 14

A car rental company charges a flat fee of $$\20$ plus $$\$$0.50$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles driven?

Accepted Answer

$$C = 0.5m + 20$$

Question 15

Find the slope of the line $$4x + 3y = 12.$$

Accepted Answer

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

Question 16

Which of the following is the average rate of change of $$f(x)$$ from $$x = 0 to$$ $$x = 2.5 if$$ $$f(0) = 2$$ and $$f(2.5) = 1$$?

Accepted Answer

$$\frac{1 - 2}{2.5 - 0} = -0.4$$

Question 17

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

Accepted Answer

$$y = 5x + 13$$

Question 18

Which of the following is the correct interpretation of the slope in the context of a real-world problem?

Accepted Answer

The slope represents the rate of change between two variables.

Question 19

If a line has a slope of $$\frac{2}{3}$$, how do you move from one point to another on the line?

Accepted Answer

Up 2 units, right 3 units

Question 20

Which of the following equations represents a line with a $$y-$$intercept of $$5$$ and a slope of $$-\frac{5}{3}$$?

Accepted Answer

$$y = -\frac{5}{3}x + 5$$

Linear Equations in Two Variables and Functions: Graphs, Slope, and Rate of Change

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