Question 1

A company charges a base fee of $$50 plus 20 $$per hour for consulting services. Which equation best models the total cost $$C as a $$function of hours $$h$$?

Accepted Answer

$$C(h) = 20h + 50$$

Question 2

Given the line $$y = -\frac{3}{2}x + 4$$, what is the $$x-$$intercept of the line?

Accepted Answer

$$(\frac{8}{3}, 0)$$

Question 3

Which of the following best describes the slope of the line $$y = -\frac{3}{2}x + 4$$?

Accepted Answer

The slope is negative, so the line is slanted downward.

Question 4

A straight line passes through the points $$(2, 5)$$ and $$(6, 1). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = -x + 7$$

Question 5

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 6

If a line has the equation $$4x + 7y = 24$$, what is its slope?

Accepted Answer

$$m = -\frac{4}{7}$$

Question 7

A biologist tracks the population of a species over time and finds it decreases by 15 animals per year, starting from 200 animals. Which equation models the population $$P$$ after $$t$$ years?

Accepted Answer

$$P(t) = -15t + 200$$

Question 8

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

Accepted Answer

The $$y-$$intercept of the line

Question 9

Which of the following is the standard form of a linear equation?

Accepted Answer

$$Ax + By = C$$

Question 10

A line passes through $$(-4, -7)$$ and has a slope of $$\frac{5}{3}. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = \frac{5}{3}x + \frac{41}{3}$$

Question 11

If a line has a slope of $$0$$, what is the equation of the line?

Accepted Answer

$$y = b$$

Question 12

Which of the following statements about the range of a linear function $$f(x) = mx + b is $$correct?

Accepted Answer

The range is $$\mathbb{R} ($$all real numbers)

Question 13

A line passes through the points $$(-3, 2)$$ and $$(5, 9). $$What is the slope of the line?

Accepted Answer

$$\frac{7}{8}$$

Question 14

Which of the following is the point-slope form of the equation of a line?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 15

A medical researcher finds that the temperature $$T (in$$ $$^0C) of a $$patient decreases at a constant rate of $$0.2^0C $$per hour after taking medication, starting from $$38^0C. $$Which equation models the temperature after $$h$$ hours?

Accepted Answer

$$T(h) = -0.2h + 38$$

Question 16

If a line has the equation $$y = 7x - 3$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -3)$$

Question 17

Which of the following is NOT a valid form for the equation of a straight line?

Accepted Answer

$$y = mx^2$ + b$$

Question 18

A line passes through $$(0, b)$$ and has slope $$m. $$Which equation represents this line?

Accepted Answer

$$y = mx + b$$

Question 19

A chemist mixes a solution at a constant rate, increasing the concentration by $$0.5$$ grams per minute. If the initial concentration is $$2$$ grams, what is the concentration $$C$$ after $$t$$ minutes?

Accepted Answer

$$C(t) = 0.5t + 2$$

Question 20

Which of the following statements is true for any non-vertical, non-horizontal straight line?

Accepted Answer

The domain and range are both $$\mathbb{R}$$

Linear Functions and Equations of Lines: Forms, Properties, and Applications

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