Question 1

Which of the following best describes the slope of a line that is perpendicular to a line with slope $$m = 2$$?

Accepted Answer

$$m = -\frac{1}{2}$$

Question 2

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

Accepted Answer

$$m = 2$$

Question 3

A company’s cost to produce $$x$$ shirts is modeled by $$C(x) = 7.5x + 550. If $$each shirt sells for $$15$$, what is the revenue equation $$R(x)$$?

Accepted Answer

$$R(x) = 15x$$

Question 4

What is the break-even point for Sassy Surf Creations, where revenue equals cost, given $$C(x) = 7.5x + 550$$ and $$R(x) = 15x$$?

Accepted Answer

$$x = 73.33$$

Question 5

If the slope of a line is undefined, which of the following best describes the line?

Accepted Answer

Vertical

Question 6

Which equation represents a line parallel to $$y = -3x + 7$$?

Accepted Answer

$$y = -3x - 2$$

Question 7

Given the cost equation $$C(x) = 7.5x + 550$$ and the revenue equation $$R(x) = 15x$$, what is the profit equation $$P(x)$$?

Accepted Answer

$$P(x) = 15x - 7.5x - 550$$

Question 8

If a line passes through the points $$(1, 4)$$ and $$(5, 12)$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = 2x + 2$$

Question 9

A horizontal line passes through the point $$(3, -2). $$What is its equation?

Accepted Answer

$$y = -2$$

Question 10

If the average rate of change of a function $$f(x)$$ from $$x = 1 to$$ $$x = 4 is$$ $$5$$, which of the following is true?

Accepted Answer

$$\frac{f(4) - f(1)}{4 - 1} = 5$$

Question 11

Which of the following statements is true about parallel lines?

Accepted Answer

They have the same slope.

Question 12

A line has the equation $$y = 4x - 9. $$What is the slope of a line perpendicular to it?

Accepted Answer

$$m = -\frac{1}{4}$$

Question 13

If the cost to produce $$x$$ items is $$C(x) = 7.5x + 550$$ and you produce 200 items, what is the total cost?

Accepted Answer

$$C(200) = 2050$$

Question 14

Which of the following best describes the behavior of a line with $$m \u003c 0$$?

Accepted Answer

Decreasing

Question 15

If $$y = mx + b$$ and $$m = 0$$, what is the graph of the line?

Accepted Answer

A horizontal line

Question 16

A company’s profit equation is $$P(x) = 7.5x - 550. $$What does the $$-550$$ represent?

Accepted Answer

The fixed costs

Question 17

If two lines are neither parallel nor perpendicular, what are they called?

Accepted Answer

Skewed

Question 18

Which of the following is the correct formula for the slope between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 19

If the revenue equation is $$R(x) = 15x$$ and the cost equation is $$C(x) = 7.5x + 550$$, what is the profit when 100 shirts are sold?

Accepted Answer

$$P(100) = 200$$

Question 20

Which of the following best describes the average rate of change of a function $$f(x)$$ between $$x = a$$ and $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Linear Functions and Slope: Study Notes for Precalculus

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