# What is the equation in y=mx+b of the line through points (0,3) , (5,-3)?

Jun 22, 2015

$y = - \frac{6}{5} x + 3$

#### Explanation:

First evaluate the slope $m$ as:
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 3 - 3}{5 - 0} = - \frac{6}{5}$

Then you can use the realtionship:

$y - {y}_{0} = m \left(x - {x}_{0}\right)$

Where we can choose the coordinates of, say, the first point to be (${x}_{0} , {y}_{0}$):
$y - 3 = - \frac{6}{5} \left(x - 0\right)$
$y = - \frac{6}{5} x + 3$ which is in the form $y = m x + b$