Question 1

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

Accepted Answer

$$m = 2$$

Question 2

Which of the following equations represents a horizontal line?

Accepted Answer

$$y = 4$$

Question 3

A road rises 8 feet for every 200 feet of horizontal distance. What is the grade of the road as a percentage?

Accepted Answer

$$4\%$$

Question 4

Which of the following is NOT a function?

Accepted Answer

$$x = 3$$

Question 5

If a line has the equation $$y = -\frac{2}{3}x + 4$$, what is its y-intercept?

Accepted Answer

$$(0, 4)$$

Question 6

A female child's adult height $$F(x) in $$inches is estimated by $$F(x) = 0.5x - 2.5$$, where $$x is $$the sum of her parents' heights in inches. If her parents' combined height is $$130$$ inches, what is her estimated adult height?

Accepted Answer

$$62.5$$ inches

Question 7

What is the average rate of change in the number of participants if a program grows from $$20$$ million to $$44$$ million over $$12$$ years?

Accepted Answer

$$2$$ million per year

Question 8

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

Accepted Answer

The slope is undefined

Question 9

Given the linear function $$f(x) = 7$$, which of the following statements is true?

Accepted Answer

The graph is a horizontal line with slope $$0$$

Question 10

If the equation of a line is $$3x - 6y - 7 = 0$$, what is its slope?

Accepted Answer

$$\frac{1}{2}$$

Question 11

A line passes through the points $$(1, 2)$$ and $$(4, 8). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 2x$$

Question 12

Which of the following best describes the identity function?

Accepted Answer

$$f(x) = x$$

Question 13

A curb ramp rises $$3$$ inches over a horizontal run of $$36$$ inches. What is the slope of the ramp as a decimal?

Accepted Answer

$$0.083$$

Question 14

If a line has a negative slope, which of the following is true about its graph?

Accepted Answer

It slants down from left to right

Question 15

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

Accepted Answer

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

Question 16

A linear function $$f(x)$$ has a slope of $$0$$ and passes through the point $$(5, -2). $$What is its equation?

Accepted Answer

$$f(x) = -2$$

Question 17

If the equation of a line is $$y = 0.25x - 3.8$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$0.25$$, y-intercept: $$(0, -3.8)$$

Question 18

A company’s revenue increases from $$\50$$,000$$ to $$\$$110,000$$ over $$5$$ years. What is the average rate of change in revenue per year?

Accepted Answer

$$\12$$,000$ per year

Question 19

Which of the following statements about linear functions is correct?

Accepted Answer

A linear function can be written as $$f(x) = mx + b$$ where $$m$$ and $$b$$ are constants.

Question 20

If the average rate of change of a population is $$-1,500$$ people per year over a decade, what does this indicate?

Accepted Answer

The population is decreasing by $$1,500$$ people each year.

Linear Functions, Slope, and Applications – Precalculus Study Notes

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