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 $^0$C) of a patient decreases at a constant rate of $0.2^0$C per hour after taking medication, starting from $38^0$C. 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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