# How do you write the equation of a line given (-3,2) (3,6)?

Feb 22, 2017

$y = \frac{2}{3} x + 4$

#### Explanation:

$\left(- 3 , 2\right) \mathmr{and} \left(3 , 6\right)$
$y = m x + b$

For $m$, which is slope

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = m \text{ (slope)}$

so

$\frac{6 - 2}{3 - \left(- 3\right)} = \frac{4}{6} = \frac{2}{3} = m$

$y = \frac{2}{3} x + b$

for b - use one of the points for $\left(x , y\right)$

$y = \frac{2}{3} x + b$
$6 = \frac{2}{3} \left(3\right) + b$
$6 = 2 + b$

$4 = b$

Now we have $m \mathmr{and} b$