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

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