# Tutoring math, you know this skill is essential.  The math tutor provides a quick explanation and example.

The concept of slope is known to all in everyday life.  In math, it is defined as follows:

(1)

Indeed, slope is often referred to as . The rise refers to the change in height; the run, to the change in horizontal position.

This article assumes you understand points on the cartesian plane. If you don’t, see my article here.

Example: Let’s imagine you need the slope of the line pictured here:

We need to realize three facts:

1) Every point is (x,y); x means horizontal position, while y means vertical.

2) “Change” means the final value minus the initial value.

3) Once again, the rise refers to the change in height; the run, to the change in horizontal position.

Now we invoke the equation for slope:

(2)

Notice that means “the first point”, while means “the second point.” It’s helpful to label your two points and . Next, carefully insert the values in their right places in the equation:

(3)

Simplifying, we get

(4)

Slope is always pictured from left to right. If a line rises to the right, its slope is positive. The line in our example falls to the right; hence, its slope is negative.

The slope of a line has many applications, which I’ll be discussing in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.