# How do you determine the standard form of the equation of the line that passes through (-7, 8) and (0, -8)?

Apr 25, 2018

$6 x + 7 y = - 56$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where A is a positive integer and B, C are integers}$

$\text{obtain the equation in "color(blue)"point-slope form}$

•color(white)(x)y-y_1=m(x-x_1)

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-7,8)" and } \left({x}_{2} , {y}_{2}\right) = \left(0 , - 8\right)$

$\Rightarrow m = \frac{- 8 - 8}{0 - \left(- 7\right)} = \frac{- 16}{7} = - \frac{16}{7}$

$\text{using "m=-16/7" and "(x_1,y_1)=(-7,8)" then}$

$y - 8 = - \frac{16}{7} \left(x - \left(- 7\right)\right)$

$\Rightarrow y - 8 = - \frac{16}{7} \left(x + 7\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

$\text{distribute and rearrange}$

$y - 8 = - \frac{16}{7} x - 16$

$\text{multiply all terms by 7}$

$7 y - 56 = - 16 x - 112$

$\Rightarrow 16 x + 7 y = - 56 \leftarrow \textcolor{red}{\text{in standard form}}$