# How do you write an equation in slope-intercept form of the line that passes through the points (-7,-3) and (-12,5)?

Dec 4, 2016

$y = - \frac{8}{5} x - \frac{71}{5}$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

We have to find m and b.

To find m, use the $\textcolor{b l u e}{\text{gradient formula}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) \text{ are 2 coordinate points}$

The 2 points here are (-7 ,-3) and (-12 ,5)

let $\left({x}_{1} , {y}_{1}\right) = \left(- 7 , - 3\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 12 , 5\right)$

$\Rightarrow m = \frac{5 - \left(- 3\right)}{- 12 - \left(- 7\right)} = \frac{8}{- 5} = - \frac{8}{5}$

We can now write the partial equation $y = - \frac{8}{5} x + b$

To find b, substitute either of the 2 given points into the
partial equation

Choosing (-12 ,5) that is x = - 12 and y = 5

$5 = \left(- \frac{8}{5} \times - 12\right) + b$

$\Rightarrow 5 = \frac{96}{5} + b \Rightarrow b = 5 - \frac{96}{5} = \frac{25}{5} - \frac{96}{5} = - \frac{71}{5}$

$\Rightarrow y = - \frac{8}{5} x - \frac{71}{5} \text{ is the equation of the line}$