# How do you determine the slope of the line passing through (2, –5) and (–1, –1)?

Jun 19, 2015

slope = (change in $y$) / (change in $x$) $= - \frac{4}{3}$

#### Explanation:

If a line passes through $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ then it's slope is given by the formula:

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

In our example,

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

so

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

$= \frac{- 1 - \left(- 5\right)}{- 1 - 2} = \frac{4}{- 3} = - \frac{4}{3}$