In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. In this sub-topic we will learn about slope (also known as gradient).

The steepness or slope of a line in the xy-coordinate system is the ratio of the vertical rise (the change in y-coordinates) to the horizontal run (the change in x-coordinates) between two points on the line.

The gradient (also known as slope) of a line is defined as:

The gradient (or slope) of the line AB is given by

In general, if (x₁, y₁) and (x₂, y₂) are the coordinates of two points, then the vertical rise is y₂ - y₁ and the run is x₂ - x₁. Thus, the gradient or slope of the line joining the points (x₁, y₁) and (x₂, y₂) is given by

Slope is often denoted by the letter m.

Remark

In the next sections you will see that there are tabular values which are used to find trigonometric values of an angle θ.

Like sin θ, cos θ or tan θ.

We can also use Scientific calculators to find trigonometric values.

For the purpose of this section we can use this small table of find trigonometric values of some special angles.