Question 1

Given two points $A(2, 5)$ and $B(6, 13)$ on a line, what is the slope $m$ of the line passing through these points?

Accepted Answer

$m = \frac{13 - 5}{6 - 2} = 2$

Question 2

Which of the following best describes the equation $y = 7$?

Accepted Answer

A horizontal line with slope $0$

Question 3

A company’s cost function is $C(x) = 8x + 1200$. What is the marginal cost?

Accepted Answer

$8$

Question 4

If the revenue function is $R(x) = 15x$ and the cost function is $C(x) = 10x + 200$, what is the break-even quantity?

Accepted Answer

$x = 40$

Question 5

Which of the following statements about the slope of a line is correct?

Accepted Answer

The slope is undefined for vertical lines.

Question 6

A business sells a product for $p = 25$ dollars per unit. If $q$ units are sold, which equation represents the revenue function?

Accepted Answer

$R(q) = 25q$

Question 7

Given the point $(4, -3)$ and a slope $m = 2$, what is the equation of the line in point-slope form?

Accepted Answer

$y + 3 = 2(x - 4)$

Question 8

If a company’s profit function is $P(x) = 12x - 500$, what is the minimum number of units $x$ that must be sold to make a profit?

Accepted Answer

$x = 42$

Question 9

Which of the following is the correct interpretation of the $y$-intercept in the cost function $C(x) = 7x + 350$?

Accepted Answer

The fixed cost is $350$

Question 10

Suppose the supply and demand equations for a product are $q_s = 4p - 20$ and $q_d = 100 - 2p$. What is the equilibrium price?

Accepted Answer

$p = 20$

Question 11

Which equation represents a vertical line passing through $x = -3$?

Accepted Answer

$x = -3$

Question 12

A company’s cost function is $C(x) = 5x + 1000$ and its revenue function is $R(x) = 12x$. What is the profit function $P(x)$?

Accepted Answer

$P(x) = 7x - 1000$

Question 13

If the equation of a line is $y = -4x + 9$, what is the slope and $y$-intercept?

Accepted Answer

Slope $= -4$, $y$-intercept $= 9$

Question 14

Which of the following best describes the break-even point for a business?

Accepted Answer

The point where revenue equals cost

Question 15

A company’s revenue function is $R(x) = 20x$ and its cost function is $C(x) = 15x + 300$. What is the profit when $x = 50$ units?

Accepted Answer

$P(50) = 250$

Slopes and Equations of Lines: Linear Functions in Business Calculus

Study Guide - Practice Questions