### All ACT Math Resources

## Example Questions

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

Find the slope of the following line: 6*x –* 4*y *= 10

**Possible Answers:**

1.5

–5/2

–1.5

5/2

**Correct answer:**

1.5

Putting the equation in *y* = *mx* + *b* form we obtain *y* = 1.5*x* – 2.5.

The slope is 1.5.

### Example Question #2 : X And Y Intercept

What is the x-intercept of the line in the standard coordinate plane for the following equation?

**Possible Answers:**

2

12

3

-24

**Correct answer:**

2

This question is asking us to find the x-intercept. Remember that the y-value is equal to zero at the x-intercept. Substitute zero in for the y-variable in the equation and solve for the x-variable.

Add 2 to both sides of the equation.

Divide both sides of the equation by 6.

The line crosses the x-axis at 2.

### Example Question #3 : X And Y Intercept

What is the equation of a line that has an x-intercept of 4 and a y-intercept of -6?

**Possible Answers:**

**Correct answer:**

The equation of a line can be written in the following form:

In this formula, *m *is the slope, and *b* represents the y-intercept. The problem provides the y-intercept; therefore, we know the following information:

We can calculate the slope of the line, because if any two points on the function are known, then the slope can be calculated. Generically, the slope of a line is defined as the function's rise over run, or more technically, the changes in the y-values over the changes in the x-values. It is formally written as the following equation:

The problem provides the two intercepts of the line, which can be written as and . Substitute these points into the equation for slope and solve:

.

Substitute the calculated values into the general equation of a line to get the correct answer:

.

### 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), (1, 0)

(0, 0), (0, 0)

(0, –2), (2, 0)

(0, –2), (–2, 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 #2 : How To Find X Or Y Intercept

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

*y* = –3*x* + 12

**Possible Answers:**

2

–1/4

–4

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 #3 : 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 #4 : How To Find X Or 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 #5 : 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 #6 : 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 #7 : 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).