Mar 17, 2018

Slope$= m = 0$

Explanation:

There are two ways to determine the slope:

One way is to just look at the graph. We have a horizontal line which means that the slope of this line, or any horizontal line for that matter will always be zero!

Another way is through some algebra which will actually prove the statement above.

You may have heard of the slope formula which states:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Where
$\cdot$ $m$ is the slope of the line

$\cdot$ $\left({x}_{1} , {y}_{1}\right)$ is a point on the line

$\cdot \left({x}_{2} , {y}_{2}\right)$ is a second point on the same line

So...

We have the points $\left(- 2 , - 5\right)$ and $\left(4 , - 5\right)$ so we'll say

$\left({x}_{1} , {y}_{1}\right) \to \left(- 2 , - 5\right)$

$\left({x}_{2} , {y}_{2}\right) \to \left(4 , - 5\right)$

So we'll plug in into the slope formula

$m = \frac{- 5 - \left(- 5\right)}{4 - \left(- 2\right)} = \frac{0}{6} = 0$

So there you have it. The slope of the line is $0$