Gradients and Lines with Same Gradient

Key points

The gradient, also known as the slope, of a line, is a measure of both the direction and steepness of a line.
- It is calculated by dividing its vertical change by its horizontal change: “rise over run”.
- You need at least two points on a line to find its slope.
Lines with the same slope are either the same line, or lines that are parallel and will never meet.

The Gradient , or slope of a line is a measure of how “steep” a line is, and the direction it is in.

The greater the value of the slope, the more “steep” it is.
A positive slope means the line goes from the bottom left towards the top right.
A negative slope means the line goes from the top left to the bottom right.
If the slope is 0, then the line is horizontal. If it is undefined, then the line is vertical.

Calculating the slope of a line is very simple:

With at least two points on the line:
- Find the change of the y coordinates (delta y) by subtracting one of the y values from the other.
- Find the change of the x coordinates (delta x) by subtracting one of the x values from the other.
  - Make sure that you are subtracting corresponding coordinates from the other.
- Divide the change in y by the change in x.
Commonly remembered as “rise over run”.
If there is no change in x, then the line is a vertical line with undefined slope.

Lines with the same slope are:

The same line, if they have the same y intercept.
Parallel lines, if they have different y-intercepts.
- They will run alongside each other, but will never get any further or closer each other because they have the same slope.
In this example, the line on the left is when the lines have different intercepts, and the right is when they have the same intercept.