### Slope

Calculating slope is one of the most important skills that you will need for coordinate geometry problems on your test.

The formula for the slope of a line is as follows:

*y* = *mx* + *b*

Remember that *m* is the slope and *b* is the y intercept.

Try these free exercises.

**Problem 1:**

Consider a line that crosses the *y* axis at 10 and upon which lies point (6, 4). What is the slope of this line?

A. − 1

B. 1

C. − 6

D. 6

E. 10

**The correct answer is A.**

*y* = *mx* + *b*

Remember that *m* is the slope and *b* is the y intercept.

We have got point (6, 4), so we can substitute those values for a and y.

4 = *m6* + 10

4 − 10 = *m6* + 10 − 10

− 6 = *m6*

− 1 = *m*

**Problem 2:**

Marta has just bought a new pair of tennis shoes. She wants to wear the new running shoes to run up and down a hill near her house.

The measurements to find the slope of the hill can be placed on a two dimensional linear graph on which *x* = 5 and *y* = 165.

If the line crosses the *y* axis at 15, what is the slope of this hill?

A. 10

B. 20

C. 30

D. 36

E. 75

**The correct answer is C.**

In order to calculate the slope of a line, you need this formula:

*y* = *mx* + *b*

Again remember that *m* is the slope and *b* is the y intercept.

Now substitute the values:

*y* = *mx* + *b*

165 = *m*5 + 15

165 − 15 = *m*5 + 15 − 15

150 = *m*5

150 ÷ 5 = *m*5 ÷ 5

30 = *m*

Have a look at our other **geometry problems**.

Go ahead to our free sample ACT **math test**.