Question 1

Given the points $$A(2, 9)$$ and $$B(5, 3)$$, what is the equation of the line passing through these points in slope-intercept form?

Accepted Answer

$$y = -2x + 13$$

Question 2

A company has a fixed cost of $$7145 and the total cost to produce 100 widgets is 7965. $$What is the marginal cost per widget?

Accepted Answer

$$8.20$$

Question 3

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

Accepted Answer

Undefined

Question 4

If the demand function for watermelons is $$p = 10 - 0.85q$$ and the supply function is $$p = 0.4q$$, what is the equilibrium quantity?

Accepted Answer

$$q = 8$$

Question 5

What is the equation of a line parallel to $$y = \frac{1}{2}x + 3$$ that passes through the point $$(4, 5)$$?

Accepted Answer

Question 6

A firm’s cost function is $$C(x) = 20x + 100$$ and the revenue function is $$R(x) = 24x. $$What is the break-even quantity?

Accepted Answer

$$x = 25$$

Question 7

Which of the following is the correct point-slope form for a line with slope $$m$$ passing through $$(x_1$, y_1$)$$?

Accepted Answer

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

Question 8

If the equation of a line is $$8x + 3y = 5$$, what is the slope of the line?

Accepted Answer

$$-\frac{8}{3}$$

Question 9

Which of the following statements is true about parallel lines?

Accepted Answer

They have the same slope.

Question 10

Given the cost function $$C(x) = 15x + 730$$, what is the fixed cost?

Accepted Answer

$$730$$

Question 11

If the supply function is $$p = 0.75q$$ and the price is $$3.30$$, how many units are supplied?

Accepted Answer

$$4400$$

Question 12

Which of the following is the correct formula for the revenue function $$R(x) if$$ $$p is $$the price per unit and $$x is $$the number of units sold?

Accepted Answer

$$R(x) = px$$

Question 13

A line passes through $$(3, 2)$$ and is perpendicular to the line $$2x + 3y = 4. $$What is the slope of the new line?

Accepted Answer

$$\frac{3}{2}$$

Question 14

Which of the following is the correct intercept-intercept form of a line with x-intercept $$a$$ and y-intercept $$b$$?

Accepted Answer

$$\frac{x}{a} + \frac{y}{b} = 1$$

Question 15

If $$F is $$the temperature in Fahrenheit and $$C is $$the temperature in Celsius, which equation correctly relates $$F$$ and $$C$$?

Accepted Answer

$$F = \frac{9}{5}C + 32$$

Question 16

A horizontal line has which of the following properties?

Accepted Answer

Slope is zero

Question 17

If the profit function is $$P(x) = R(x) - C(x)$$, what does the break-even point represent?

Accepted Answer

Where revenue equals cost

Question 18

Given the function $$g(x) = 4x - 5$$, what is $$g(-5)$$?

Accepted Answer

$$-25$$

Question 19

If a line has a slope of $$0$$, which of the following is true?

Accepted Answer

The line is horizontal

Question 20

If the demand for a product is given by $$p = 9 - 0.75q$$, what happens to the quantity demanded as the price decreases?

Accepted Answer

It increases

Business Calculus: Linear Functions and Their Applications

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