# Slope

### Slope – ACT Math

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

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

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 = m5 + 15

165 − 15 = m5 + 15 − 15

150 = m5

150 ÷ 5 = m5 ÷ 5

30 = m

Have a look at our other geometry problems.

Go ahead to our free sample ACT math test.