# How do you write an equation in standard form given point (3,3) and (1,-3)?

Jun 20, 2017

$3 x - y = 6$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where A is a positive integer and B, are integers.

$\text{express the equation initially in "color(blue)"slope-intercept form}$

• y=mx+b

#"where m represents the slope and b the y-intercept.

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

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

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

$\Rightarrow m = \frac{- 3 - 3}{1 - 3} = \frac{- 6}{- 2} = 3$

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

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

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

$3 = 9 + b \Rightarrow b = - 6$

$\Rightarrow y = 3 x - 6 \leftarrow \textcolor{red}{\text{ in [slope-intercept form](https://socratic.org/algebra/graphs-of-linear-equations-and-functions/slope-intercept-form)}}$

$\text{rearrange equation into standard form}$

$\Rightarrow 3 x - y = 6 \leftarrow \textcolor{red}{\text{ in standard form}}$