How do you write an equation in standard form given point (-2,2) and (-5,5)?

Apr 11, 2018

$x + y = 0$

Explanation:

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

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

$\text{where A is a positive integer and B, C are integers}$

$\text{obtain the equation first of all in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-2,2)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 5 , 5\right)$

$\Rightarrow m = \frac{5 - 2}{- 5 - \left(- 2\right)} = \frac{3}{- 3} = - 1$

$\Rightarrow y = - x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(-2,2)" then}$

$2 = 2 + b \Rightarrow b = 0$

$\Rightarrow y = - x \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\Rightarrow x + y = 0 \leftarrow \textcolor{red}{\text{in standard form}}$