Slope

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 = 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.