Question 1

What is the average rate of change of $$f(x) = x^2$ + 2x$$ from $$x_1 = 3$ to x_2$ = 5$$?

Accepted Answer

$$14$$

Question 2

Which of the following is the equation of a line passing through $$(3, 5)$$ and $$(8, 15)$$?

Accepted Answer

$$y = 2x - 1$$

Question 3

Given $$f(x) = -2x + 1$$, what is the slope and y-intercept of the function?

Accepted Answer

Slope: $$-2$$, y-intercept: $$1$$

Question 4

A line passes through $$(-2, 2)$$ and $$(2, 2). $$What is the slope of this line, and how does the line behave?

Accepted Answer

Slope: $$0$$, the line is horizontal.

Question 5

Find the equation of the line passing through $$(2, -3)$$ and perpendicular to $$y = \frac{1}{3}x + 6.$$

Accepted Answer

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

Question 6

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

Accepted Answer

$$y = -2x + 10$$

Question 7

Given the function $$f(x) = \sqrt{x}$$, what is the average rate of change from $$x_1 = 4$ to x_2$ = 9$$?

Accepted Answer

$$1$$

Question 8

Rewrite the equation $$6x - 2y - 12 = 0 in $$slope-intercept form.

Accepted Answer

$$y = 3x - 6$$

Question 9

A line passes through $$(4, -1)$$ and $$(3, -1). $$What is the slope and the behavior of the line?

Accepted Answer

Slope: $$0$$, the line is horizontal.

Question 10

Find the equation of the line passing through $$(-1, 3)$$ and parallel to $$3x - 2y - 5 = 0 in $$point-slope form.

Accepted Answer

Question 11

Given $$f(x) = -\frac{3}{5}x + 7$$, what is the y-intercept of the function?

Accepted Answer

$$7$$

Question 12

What is the slope of the line passing through the points $$(4, 7)$$ and $$(8, 10)$$?

Accepted Answer

Question 13

Which of the following equations represents a line perpendicular to $$y = -2x$$ and passing through $$(-1, 2)$$?

Accepted Answer

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

Question 14

Given $$f(x) = 3x$$ from $$x_1 = 0$ to x_2$ = 5$$, what is the average rate of change?

Accepted Answer

$$3$$

Question 15

Find the equation of the line passing through $$(5, -9)$$ and perpendicular to $$x + 7y - 12 = 0 in $$point-slope form.

Accepted Answer

$$y + 9 = -7(x - 5)$$

Question 16

Given $$f(x) = 6x$$ from $$x_1 = 0$ to x_2$ = 4$$, what is the average rate of change?

Accepted Answer

$$6$$

Question 17

Which of the following is the correct equation for a line parallel to $$y = -5x + 4$$ and passing through $$(-2, -7)$$?

Accepted Answer

$$y + 7 = -5(x + 2)$$

Question 18

Given the equation $$3x + 5y + 15 = 0$$, what is the y-intercept?

Accepted Answer

Question 19

What is the average rate of change of $$f(x) = x^2$ - 2x$$ from $$x_1 = 3$ to x_2$ = 6$$?

Accepted Answer

$$12$$

Linear Functions, Slope, and Rate of Change – Precalculus Study Guidance

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