# How do you write an equation in standard form for a line which passes through points (-1,-1) and (1,3)?

Jul 2, 2018

$2 x - y = - 1$

#### Explanation:

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

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

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

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

•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)

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

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

$y = 2 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(1,3)" then}$

$3 = 2 + b \Rightarrow b = 3 - 2 = 1$

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

$\text{rearranging gives}$

$2 x - y = - 1 \leftarrow \textcolor{red}{\text{in standard form}}$