Question 1

Which of the following is the correct definition of the x-intercept of a graph?

Accepted Answer

The x-coordinate of a point where the graph intersects the x-axis, with y always zero.

Question 2

Given the equation $$4x - 3y = 12$$, what is the y-intercept of its graph?

Accepted Answer

$$y = -4$$

Question 3

A company tracks its profit using the equation $$2x + 3y = 6$$, where $$x is $$the number of products sold and $$y is $$the advertising budget in thousands of dollars. What is the x-intercept, and what does it represent in this context?

Accepted Answer

$$x = 3$$, representing the number of products sold when the advertising budget is zero.

Question 4

Which of the following equations represents a vertical line?

Accepted Answer

$$x = -2$$

Question 5

If a line passes through the origin and has the equation $$x + 3y = 0$$, what are its x- and y-intercepts?

Accepted Answer

Both intercepts are $$0.$$

Question 6

Which of the following best describes the graph of $$y = 3$$?

Accepted Answer

A horizontal line crossing the y-axis at $$y = 3.$$

Question 7

Find the x-intercept of the equation $$5x - 2y = 10.$$

Accepted Answer

$$x = 2$$

Question 8

A biologist models the population of a species with $$3x + 2y = 12$$, where $$x is $$the number of years and $$y is $$the population in hundreds. What is the y-intercept, and what does it represent?

Accepted Answer

$$y = 6$$, representing the initial population when $$x = 0.$$

Question 9

Which of the following statements is true about the graph of $$Ax + By = C$$ when $$A$$ and $$B$$ are not both zero?

Accepted Answer

It is always a straight line.

Question 10

Given the equation $$2x + 3y = 6$$, what is a checkpoint (third solution) you could use to graph the line?

Accepted Answer

$$(1, \frac{4}{3})$$

Question 11

A vertical line is graphed as $$x = a. $$Which of the following is true about its intercepts?

Accepted Answer

It has an x-intercept at $$(a, 0)$$ and no y-intercept unless $$a = 0.$$

Question 12

If the equation of a line is $$y = 0$$, what kind of line is it and where does it cross the axes?

Accepted Answer

A horizontal line crossing the x-axis at all points where $$y = 0.$$

Question 13

Which of the following is the correct process to find the x-intercept of $$Ax + By = C$$?

Accepted Answer

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

Question 14

A medical researcher uses $$x + 2y = 8 to $$model a relationship between dosage ($$x) $$and patient response ($$y). $$What is the y-intercept and what does it represent?

Accepted Answer

$$y = 4$$, representing the patient response when dosage is zero.

Question 15

Which of the following equations represents a horizontal line?

Accepted Answer

$$y = 5$$

Graphing Linear Equations and Identifying Intercepts

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