# How do you write an equation of a line given (1,-3) and (-2,-4)?

Jun 17, 2017

$y = \frac{1}{3} x - \frac{10}{3}$

#### 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 $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) \text{ are 2 points}$

$\text{the points are } \left({x}_{1} , {y}_{1}\right) = \left(1 , - 3\right) , \left({x}_{2} , {y}_{2}\right) = \left(- 2 , - 4\right)$

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

$\Rightarrow y = \frac{1}{3} x + b \leftarrow \text{ is partial equation}$

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

$\text{using } \left(1 , - 3\right)$

$- 3 = \frac{1}{3} + b \Rightarrow b = - 3 - \frac{1}{3} = - \frac{10}{3}$

$\Rightarrow y = \frac{1}{3} x - \frac{10}{3} \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$