Question 1

Which of the following best describes the effect of adding a constant to a linear function $$f(x) = mx to $$create $$g(x) = mx + b$$?

Accepted Answer

The graph of $$g(x) is $$shifted upward by $$b$$ units compared to $$f(x).$$

Question 2

Given the equation $$y = 4x - 8$$, what are the x- and y-intercepts?

Accepted Answer

x-intercept: $$(2, 0)$$, y-intercept: $$(0, -8)$$

Question 3

How do you find the x-intercept of a linear equation in the form $$y = mx + b$$?

Accepted Answer

Set $$y = 0$$ and solve for $$x.$$

Question 4

A company’s profit $$P (in $$dollars) can be modeled by the linear function $$P(x) = 50x - 200$$, where $$x is $$the number of units sold. What is the break-even point (where profit is zero)?

Accepted Answer

$$x = 4$$

Question 5

Which of the following equations represents a vertical line?

Accepted Answer

$$x = -3$$

Question 6

If a line passes through the origin and has a slope of $$2$$, which equation represents this line?

Accepted Answer

$$y = 2x$$

Question 7

A horizontal line passes through the point $$(0, 5). $$Which equation describes this line?

Accepted Answer

$$y = 5$$

Question 8

Given the equation $$4 = x - 3y$$, what is the y-intercept?

Accepted Answer

$$(0, -\frac{4}{3})$$

Question 9

Which of the following statements is true about the graph of $$y = c$$, where $$c is a $$real number?

Accepted Answer

It is a horizontal line with y-intercept $$(0, c).$$

Question 10

A line has the equation $$y = -2x + 6. $$What is the y-intercept and what does it represent in a real-world context?

Accepted Answer

The y-intercept is $$(0, 6)$$, representing the initial value when $$x = 0.$$

Question 11

If the graph of $$y = 2x is $$shifted upward by $$3$$ units, what is the new equation?

Accepted Answer

$$y = 2x + 3$$

Question 12

Which of the following is true about the point $$(0, 0) on $$the graph of a linear equation?

Accepted Answer

It is both an x-intercept and a y-intercept.

Question 13

A line passes through $$(0, 0)$$ and $$(2, 4). $$What is its equation?

Accepted Answer

$$y = 2x$$

Question 14

Which of the following best describes the graph of $$x = 5$$?

Accepted Answer

A vertical line passing through $$(5, 0)$$

Question 15

If a linear function models the temperature $$T (in$$ °C) as a function of time $$t (in $$hours) by $$T(t) = -3t + 18$$, what is the temperature after 4 hours?

Accepted Answer

$$6$$ °C

Question 16

Which of the following is NOT a property of the graph of a vertical line?

Accepted Answer

It has a y-intercept.

Question 17

Given the equation $$y = 0.5x - 4$$, what is the x-intercept?

Accepted Answer

$$(8, 0)$$

Question 18

A horizontal line is used to represent the water level in a tank that remains constant at 7 meters. Which equation models this situation?

Accepted Answer

$$y = 7$$

Question 19

If $$y = mx + b$$ and $$b = 0$$, what is true about the graph?

Accepted Answer

The line passes through the origin.

Graphing Linear Functions: Intercepts, Vertical and Horizontal Lines

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