# What is the equation of the line between (-11,12) and (7,-7)?

Apr 27, 2018

$y = - \frac{19}{18} x + \frac{7}{18}$

#### 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)

$\text{let "(x_1,y_1)=(-11,12)" and } \left({x}_{2} , {y}_{2}\right) = \left(7 , - 7\right)$

$\Rightarrow m = \frac{- 7 - 12}{7 - \left(- 11\right)} = \frac{- 19}{18} = - \frac{19}{18}$

$\Rightarrow y = - \frac{19}{18} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(-11,12)" then }$

$12 = \frac{209}{18} + b \Rightarrow b = \frac{216}{18} - \frac{209}{18} = \frac{7}{18}$

$\Rightarrow y = - \frac{19}{18} x + \frac{7}{18} \leftarrow \textcolor{red}{\text{equation of line}}$