What is a slope? Slope Meaning in Math

Slope Definition

In mathematical terms, we call a slope gradient. The slope of a line is the measure of how steep the line is. In mathematics, it is usually calculated by a change in the y-axis divided by a change in the x-axis.

Example: Suppose the change in the x-axis is 6 units, and the change in the y-axis is 12 units. Dividing 12/6 gives us 2. Therefore the gradient of the slope is 2.

Again, Suppose the change in the x-axis is 6 units and the change in the y-axis is 18 units. Dividing 18/6 gives us 3. Therefore the gradient of the slope is 3.

Ways to calculate a slope gradient

In mathematics, there are numerous ways to calculate a slope gradient. The method shown upwards is the easiest and most used method in mathematics.

A way to find the gradient of a line if coordinates are given is by using the formula Y2-Y1/X2-X1. Suppose you have two coordinates (3,9) and (6,18). Putting it into the formula 18-9/6-3 gives us 3. Therefore the gradient is 3.

What if a curve is given, and you need to calculate the gradient of a given point? This time you need to draw a tangent(a straight line) at that point and take two suitable coordinates. Using the formula                    

Y2-Y1/X2-X1, the gradient can be found.

Example: A tangent is drawn, and two suitable coordinates are taken. The coordinates are (12,6) and (6,3). Putting it into the formula Y2-Y1/X2-X1 gives us 0.5. Therefore the gradient is 0.5.

Line Equations with Slope

1. Point slope form denotes as y - y₁ = m(x - x₁)
2. Slope intercept form equation, y = mx + b
3. Standard form of Slope of a line is Ax + By = C