# What is the slope-intercept form of the line passing through  (-5,6)  and (4,2) ?

May 1, 2018

$y = - \frac{4}{9} x + \frac{34}{9}$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-5,6)" and } \left({x}_{2} , {y}_{2}\right) = \left(4 , 2\right)$

$\Rightarrow m = \frac{2 - 6}{4 - \left(- 5\right)} = \frac{- 4}{9} = - \frac{4}{9}$

$\Rightarrow y = - \frac{4}{9} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(4,2)" then}$

$2 = - \frac{16}{9} + b \Rightarrow b = \frac{18}{9} + \frac{16}{9} = \frac{34}{9}$

$\Rightarrow y = - \frac{4}{9} x + \frac{34}{9} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$