Question 1

Given the points $$(4, -2)$$ and $$(-1, -5)$$, what is the slope of the line passing through these points?

Accepted Answer

$$m = \dfrac{-2 - (-5)}{4 - (-1)} = \dfrac{3}{5}$$

Question 2

Which of the following is the point-slope form of the equation of a line with slope $$6$$ passing through $$(2, -5)$$?

Accepted Answer

$$(y + 5) = 6(x - 2)$$

Question 3

What is the slope-intercept form of the line with slope $$\dfrac{3}{5}$$ and $$y-$$intercept $$1$$?

Accepted Answer

$$y = \dfrac{3}{5}x + 1$$

Question 4

Which equation represents a horizontal line passing through the point $$(0, 3)$$?

Accepted Answer

$$y = 3$$

Question 5

What is the slope of a vertical line?

Accepted Answer

Undefined

Question 6

Given the general form $$3x + 6y - 12 = 0$$, what is the slope and $$y-$$intercept of the line?

Accepted Answer

Slope: $$-\dfrac{1}{2}$$, $$y-$$intercept: $$2$$

Question 7

A line passes through $$(2, 0)$$ and $$(0, -3). $$What is its equation in slope-intercept form?

Accepted Answer

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

Question 8

Which of the following lines is parallel to $$y = 3x + 1$$ and passes through $$(-2, 5)$$?

Accepted Answer

$$y = 3x + 11$$

Question 9

If a line has slope $$-\dfrac{1}{3}$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$3$$

Question 10

A company tracks the number of products sold each year. In 2010, 1200 units were sold; in 2015, 1700 units were sold. What is the average rate of change in units sold per year?

Accepted Answer

$$\dfrac{1700 - 1200}{2015 - 2010} = 100$$ units/year

Question 11

Given the function $$f(x) = x^3$, what is the average rate of change from x = -2$ to x = 0$?

Accepted Answer

$$4$$

Question 12

A scientist models the relationship between atmospheric CO$$_2 (in $$ppm) and average global temperature (in $$^	ext{o}C) $$with the function $$f(x) = 0.016x + 52.0. $$What does the slope represent in this context?

Accepted Answer

The average increase in temperature (in $$^	ext{o}C) $$per 1 ppm increase in CO$$_2$$

Question 13

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

Accepted Answer

$$Ax + By + C = 0$$

Question 14

If the equation of a line is $$2x - 3y + 6 = 0$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$(-3, 0)$$, $$y-$$intercept: $$(0, 2)$$

Question 15

Which of the following statements is TRUE about parallel lines?

Accepted Answer

Parallel lines have the same slope.

Question 16

A line passes through $$(1, 2)$$ and is perpendicular to the line $$y = -2x + 3. $$What is the equation of the line in point-slope form?

Accepted Answer

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

Question 17

Which of the following best describes the average rate of change of a function $$f$$ from $$x_1 to$$ $$x_2$$?

Accepted Answer

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

College Algebra: Linear Functions and Slope (Chapter 2 Study Notes)

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