# How do you write the equation for the line containing the points (3, 2) and (–2, 4)?

Nov 4, 2014

Let $\left({x}_{1} , {y}_{1}\right) = \left(3 , 2\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(- 2 , 4\right)$.

By Slope Formula,

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{4 - 2}{- 2 - 3} = - \frac{2}{5}$

By Point-Slope Form $y - {y}_{1} = m \left(x - {x}_{1}\right)$,

$y - 2 = - \frac{2}{5} \left(x - 3\right)$,

which is the equation of the line passing through both points.

I hope that this was helpful.