Math: Finding the slope of a line

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)   \begin{equation*}slope=m=\frac{rise}{run}\end{equation*}

Indeed, slope is often referred to as m. 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)   \begin{equation*}slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}\end{equation*}

Notice that (x_1,y_1) means “the first point”, while (x_2,y_2) means “the second point.” It’s helpful to label your two points (x_1,y_1) and (x_2,y_2). Next, carefully insert the values in their right places in the equation:

(3)   \begin{equation*}m=\frac{-25-110}{240--100}\end{equation*}

Simplifying, we get

(4)   \begin{equation*}m=\frac{-135}{340}=\frac{-27}{68}\ or\ -0.397\end{equation*}

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.

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