### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find X Or Y Intercept

What are the y and x intercepts of the given equation, respectively?

y = 2x – 2

**Possible Answers:**

(0, –2), (–2, 0)

(0, –2), (2, 0)

(0, –2), (1, 0)

(0, 2), (2, 0)

(0, 0), (0, 0)

**Correct answer:**

(0, –2), (1, 0)

The equation is already in slope-intercept form. The y-intercept is (0, –2). Plug in 0 for y and we get the x intercept of (1, 0)

### Example Question #1 : X And Y Intercept

What is the *x*-intercept of the following line?

*y* = –3*x* + 12

**Possible Answers:**

1/4

4

2

–1/4

–4

**Correct answer:**

4

The *x*-intercept occurs when the *y*-coordinate = 0.

*y* = –3*x* + 12

0 = –3*x* + 12

3*x* = 12

*x* = 12/3 = 4

### Example Question #1 : How To Find X Or Y Intercept

What is the -coordinate of the point in the standard coordinate plane at which the two lines and intersect?

**Possible Answers:**

**Correct answer:**

### Example Question #1 : X And Y Intercept

What is the -intercept of the line in the standard coordinate plane that goes through the points and ?

**Possible Answers:**

**Correct answer:**

The answer is .

The slope of the line is determined by calculating the change in over the change in .

The point-slope form of the equation for the line is then

. The -intercept is determined by setting and solving for . This simplifies to which shows that is the -interecept.

### Example Question #1 : How To Find X Or Y Intercept

What are the and -intercepts of the line defined by the equation:

**Possible Answers:**

**Correct answer:**

To find the intercepts of a line, we must set the and values equal to zero and then solve.

### Example Question #1 : How To Find X Or Y Intercept

In the standard (x, y) coordinate plane, a circle has the equation . At what points does the circle intersect the x-axis?

**Possible Answers:**

**Correct answer:**

The generic equation of a circle is (x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}, where (x_{0}, y_{0}) are the coordinates of the center and r is the radius.

In this case, the circle is centered at the origin with a radius of 8. Therefore the circle hits all points that are a distance of 8 from the origin, which results in coordinates of (8,0) and (-8,0) on the x-axis.

### Example Question #2 : How To Find X Or Y Intercept

What is the y-intercept of a line that passes through the point with slope of ?

**Possible Answers:**

**Correct answer:**

Point-slope form follows the format y - y_{1} = m(x - x_{1}).

Using the given point and slope, we can use this formula to get the equation y - 8 = -2(x + 5).

From here, we can find the y-intercept by setting x equal to zero and solving.

y - 8 = -2(0 + 5)

y - 8 = -2(5) = -10

y = -2

Our y-intercept will be (0,-2).

### Example Question #1 : How To Find X Or Y Intercept

Given the linear equation below, what are the x- and y-intercepts*,* respectively?

**Possible Answers:**

**Correct answer:**

To find the x-intercept we will need to plug in zero for the y-value.

The x-intercept will be .

To find the y-intercept we will need to plug in zero for the x-value.

The y-intercept will be .

### Example Question #2 : How To Find X Or Y Intercept

At what point do the lines and intersect?

**Possible Answers:**

**Correct answer:**

Short way:

The lines intersect somewhere because they have different slopes. Because they have the same y-intercept, they must intersect at that point.

Long way using substitution:

Plug this into

Find

### Example Question #2 : How To Find X Or Y Intercept

Find the -intercept(s) for the following equation:

**Possible Answers:**

**Correct answer:**

To find the intercepts, is set equal to . This yields:

And finally

It is important to realize that both and must be included because is also equal to . Finally, these are put into their point forms, and .

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