# Understanding Slope - Rise over Run

If you have two lines, how could you describe that one line is more steep than the other line?

You could use slope.

Slope is the measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run). The slope of a line can be positive, negative, or zero.

A positive slope indicates that the line is rising from left to right. A negative slope indicates that the line is falling from left to right. A zero slope indicates that the line is horizontal and a vertical line has an undefined slope.

The slope of a line can be calculated using the following formula:

Slope = rise / run

Where:

• rise is the vertical change between two points on the line

• run is the horizontal change between two points on the line

Let’s take a look at the slope of this line

Let’s first find the rise which is 1, 2 and the run is 1 2 3 4

So the slope is 2/4

m is used to represent slope.

As you move from left to right the line goes upward so the slope is positive.

Let's look at the rise -1,-2,-3,
and then the run is 1 the slope is -3.

Notice that as you move from left to right the line slopes downward so the slope is negative Also notice the slope is greater than the first line and you can see line is more steep.

So in summary, slope is a measure of the steepness of a line.

The greater the slope the greater the steepness of the line and smaller the slope the smaller the slope.

Slope Intercept Form