Slope of a Line Formula

Today we are going to learn how to calculate the slope of a line for linear equations. There is a slope of a line formula for linear equations to help you. Although it is important in mathematics to learn where the formula for finding the slope of a line comes from, most people just memorize the slope formula for quick and easy calculations. Finding the slope of a line is easy as we shall see.

Finding slope of a line

On the graph above, let's try to find the slop of the red line. The vertical axis is the y axis whereas the horizontal axis is the x axis. When finding the slope of a line, we want to know two values of x and corresponding two values of y. It does not matter which values of x you choose. However, for simplicity sake, let's choose x = 0 and x = 3. We choose these two points because it's easy to see the corresponding values of y for these two points.

From the graph, we see that when x is 0, y is negative 2 and when x is 3, y is also 3.

The slope formula

The slope formula is given by:

So in our example, if we let x ₁ be 0 and x ₂ be 3 and consequently y ₁ is negative or minus 2 and y ₂  is 3, we have the slope of the red line is:

So simply put, the slope of the red line is five over three or 1.66666 recurring. That's it. That's how to calculate the slope of a line.