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:
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:
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:
Simplifying, we get
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.