# What is the equation of the line that passes through (3, -7) and (-2, 4)?

Sep 10, 2017

$y = - \frac{11}{5} x - \frac{2}{5}$

#### Explanation:

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

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

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

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{let "(x_1,y_1)=(3,-7)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 , 4\right)$

$\Rightarrow m = \frac{4 - \left(- 7\right)}{- 2 - 3} = \frac{11}{- 5} = - \frac{11}{5}$

$\Rightarrow y = - \frac{11}{5} x + b \leftarrow \text{ partial equation}$

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

$\text{using } \left(- 2 , 4\right)$

$4 = \frac{22}{5} + b \Rightarrow b = - \frac{2}{5}$

$\Rightarrow y = - \frac{11}{5} x - \frac{2}{5} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$