# What is the equation of the line passing through the points (-5, 14) and (4, -4)?

Apr 12, 2018

$y = - 2 x + 4$

#### Explanation:

Use the slope formula:

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

Given $\left(- 5 , 14\right)$ and $\left(4 , - 4\right)$

Let:

$\left(\textcolor{red}{- 5} , \textcolor{b l u e}{14}\right) \to \left(\textcolor{red}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$

$\left(\textcolor{red}{4} , \textcolor{b l u e}{- 4}\right) \to \left(\textcolor{red}{{x}_{2}} , \textcolor{b l u e}{{y}_{2}}\right)$

Substituting in for the slope formula...

$m = \frac{\textcolor{b l u e}{- 4 - 14}}{\textcolor{red}{4 - \left(- 5\right)}} = \frac{\textcolor{b l u e}{- 18}}{\textcolor{red}{9}} = - 2$

Now that we have the slope $m$, we can find the equation of the line by using the point-slope formula:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Note: $\left({x}_{1} , {y}_{1}\right)$ can be either point given. I'll use the point $\left(4 , - 4\right)$

So...

$y - \left(- 4\right) = - 2 \left(x - 4\right)$

$y + 4 = - 2 \left(x - 4\right)$

We can then rewrite this equation in $y = m x + b$ form by simply solving for $y$

Doing so, one gets,

$y = - 2 x + 4$