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# Finding the Slope of a Line

(KS3, Year 8)

## The Lesson

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.## 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: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.)
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.)
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**.

## 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:## Zero Slope And Undefined Slope

A line that goes straight across has zero slope:A line that goes straight across has an undefined slope:

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