# What is the equation of the line passing through the points (4, -5) and (2,-7)?

Aug 2, 2018

$y = x - 9$

#### Explanation:

First you need to find the gradient of the line

$m = \frac{- 5 + 7}{4 - 2} = \frac{2}{2} = 1$

Then, using the point gradient formula

$y - {y}_{1} = m \left(x - {x}_{1}\right)$
where $\left({x}_{1} , {y}_{1}\right)$ can be either point and $m$ is the gradient

So, I'm using the point $\left(4 , - 5\right)$

$\left(y + 5\right) = 1 \left(x - 4\right)$

$y + 5 = x - 4$

$y = x - 9$