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Finding the Slope of a Line

(KS3, Year 8)

The slope is a measure of how steep the line is. Imagine a line is drawn on a graph. We can find the slope of the line.

How to Find the Slope of a Line

Finding the slope of a line is easy.

Question

Find the slope of the line shown below. Graph with a line example

Step-by-Step:

1

Find out how many units the line has gone up. In our example, the line goes up by 4 units.

2

Find out how many units the line has gone across. In our example, the line goes across by 2 units.

3

Divide the answer from Step 1 (4) by the answer from Step 2 (2).

Slope = How far up ÷ How far across

Slope = 4 ÷ 2

Slope = 2

Answer:

The slope of the line is 2.

A Formula to Find the Slope of a Line

The formula to find the slope is shown below: The line goes across by 2 units

Let's apply the formula to the example above.

Step-by-Step:

1

Find the change in y. Subtract the y-coordinates of the start and end of the line (or two convenient points on it.) Measure the change in y by the difference in the y-coordinates

Measure the change in y by the difference in the y-coordinates

Change in y = 5 − 1 = 4

The change in y is 4.

2

Find the change in x. Subtract the x-coordinates of the start and end of the line (or two convenient points on it.) Measure the change in x by the difference in the x-coordinates

Measure the change in x by the difference in the x-coordinates

Change in x = 2 − 0 = 2

The change in x is 2.

3

Divide the change in y (4) by the change in x (2).

Slope = Change in y ÷ Change in x

Slope = 4 ÷ 2

Slope = 2

Answer:

The slope of the line is 2.

Lesson Slides

The slider below gives a real example of how to find the slope of a line.

Postive And Negative Slopes

A positive slope means the line slopes up and to the right:

A negative slope means the line slopes down and to the right:

Fractional Slope

Slope can be a fraction, such as ½ and ¾. An improper fraction is positive, but less than 1. A slope of 1 gives a 45° line. A fractional slope is less steep than this: $fractional slope$