# How do you write an equation of a line going through (-2,-3), (2,-1)?

May 10, 2017

$y = \frac{1}{2} x - 2$

#### Explanation:

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

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

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

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

$\text{the 2 points here are "(-2,-3)" and } \left(2 , - 1\right)$

$\text{let " (x_1,y_1)=(-2,-3)" and } \left({x}_{2} , {y}_{2}\right) = \left(2 , - 1\right)$

$\Rightarrow m = \frac{- 1 - \left(- 3\right)}{2 - \left(- 2\right)} = \frac{2}{4} = \frac{1}{2}$

$\Rightarrow y = \frac{1}{2} x + b \leftarrow \text{ is the partial equation}$

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

$\text{using } \left(2 , - 1\right)$

$- 1 = \left(\frac{1}{2} \times 2\right) + b \Rightarrow b = - 2$

$\Rightarrow y = \frac{1}{2} x - 2 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$