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A line passes through the points $(-4,{-2})$ and $(4,{-8})$ . Find this line’s slope. If the slope does not exist, you may enter DNE or NONE.

Solution

To find a line’s slope, we can use the slope formula:

$\text{slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

First, we mark which number corresponds to which variable in the formula:

$(-4,{-2}) \longrightarrow (x_{1},y_{1})$

$(4,{-8}) \longrightarrow (x_{2},y_{2})$

Now we substitute these numbers into the corresponding variables in the slope formula:

$\begin{aligned} \text{slope}&=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\ &=\frac{{-8}-((-2))}{4-(-4)}\\ &=\frac{{-6}}{8}\\ &=-\frac{3}{4} \end{aligned}$

So the line’s slope is $\displaystyle{-\frac{3}{4}}$ .