Question 1

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

Accepted Answer

Parallel lines have the same slope.

Question 2

Given the line $$y = 2x + 5$$, what is the equation of the line passing through $$(1, -3)$$ and parallel to the given line?

Accepted Answer

$$y = 2x - 7$$

Question 3

If a line has a slope of $$\frac{3}{4}$$, what is the slope of a line perpendicular to it?

Accepted Answer

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

Question 4

Which of the following best describes the slope as a rate of change?

Accepted Answer

The ratio of the change in $$y to $$the change in $$x.$$

Question 5

A company’s profit increased from $$\10$$,000$$ in 2015 to $$\$$25,000 in 2020. $$What is the average rate of change of profit per year?

Accepted Answer

$$\3$$,000$ per year

Question 6

Find the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$.

Accepted Answer

$$5$$

Question 7

If $$f(x) = 2x + 1$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2$$

Question 8

Which of the following is the correct interpretation of the slope in the context of the number of adult men living alone increasing from 9 million in 1990 to 14.7 million in 2008?

Accepted Answer

The number of men living alone increased by 0.32 million per year.

Question 9

Which of the following is the equation of a line perpendicular to $$y = -\frac{1}{3}x + 2$$ and passing through $$(0, 4)$$?

Accepted Answer

$$y = 3x + 4$$

Question 10

If $$f(x) = x^2$ + 2x$$, find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x + 2 + h$$

Question 11

Which of the following statements is TRUE about perpendicular lines?

Accepted Answer

Their slopes multiply to $$-1.$$

Question 12

A horizontal line has which of the following properties?

Accepted Answer

Zero slope

Question 13

Given two points $$(2, 5)$$ and $$(6, 13)$$, what is the slope of the line passing through them?

Accepted Answer

$$2$$

Question 14

If $$f(x) = 3x - 4$$, what is the average rate of change from $$x = 2 to$$ $$x = 5$$?

Accepted Answer

$$3$$

Question 15

Which of the following is the correct formula for the average rate of change of a function $$f$$ from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$\frac{f(x_2$) - f(x_1$)}{x_2$ - x_1$}$$

Functions and Graphs: More on Slope

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