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

A company’s profit $$P (in $$dollars) is modeled by the linear function $$P(x) = 50x - 200$$, where $$x is $$the number of units sold. What does the y-intercept represent in this context?

Accepted Answer

The initial loss when no units are sold.

Question 4

Which equation represents a vertical line?

Accepted Answer

$$x = -3$$

Question 5

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

Accepted Answer

$$y = 2x$$

Question 6

How do you find the x-intercept of the equation $$3x - 6y = 12$$?

Accepted Answer

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

Question 7

Which of the following 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 8

A line passes through the points $$(0, 0)$$ and $$(3, 6). $$What is the equation of the line?

Accepted Answer

$$y = 2x$$

Question 9

Which of the following statements is correct about the intercepts of the line $$y = 5x$$?

Accepted Answer

The x-intercept and y-intercept are both at $$(0, 0).$$

Question 10

A horizontal line passes through the point $$(0, 7). $$What is its equation?

Accepted Answer

$$y = 7$$

Question 11

Which of the following best describes the graph of $$x = 2$$?

Accepted Answer

A vertical line passing through $$(2, 0)$$

Question 12

If the equation of a line is $$y = mx + b$$, what is the y-intercept?

Accepted Answer

$$(0, b)$$

Question 13

A chemist is graphing the temperature $$T (in$$ °C) of a reaction over time $$t (in $$minutes) using $$T(t) = 5t + 20. $$What does the y-intercept represent?

Accepted Answer

The initial temperature at time $$t = 0.$$

Question 14

Which of the following equations represents a line with no x-intercept?

Accepted Answer

$$y = 3$$

Question 15

A line has the equation $$4 = x - 3y. $$What is the y-intercept?

Accepted Answer

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

Question 16

Which of the following is the correct process to graph a linear equation using intercepts?

Accepted Answer

Find the x-intercept by letting $$y = 0$$, and the y-intercept by letting $$x = 0$$, then plot both points and draw the line through them.

Question 17

A medical researcher models the dosage $$D (in mg) of a $$drug over time $$t (in $$hours) as $$D(t) = -2t + 10. $$What does the x-intercept represent?

Accepted Answer

The time when the drug is completely eliminated from the body.

Question 18

Which of the following is true about the graph of $$y = 0$$?

Accepted Answer

It is a horizontal line passing through the x-axis.

Question 19

If a line passes through $$(0, -5)$$ and $$(2, 1)$$, what is its equation?

Accepted Answer

Graphing Linear Functions: Study Notes for Intermediate Algebra

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