### 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:**

5/2

–5/2

–1.5

1.5

**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 #1 : How To Find The Equation Of A Curve

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:

.