# How do you write an equation in standard form for a line passing through (9,8) and (4,7)?

##### 1 Answer
May 28, 2018

$x - 5 y = - 31$

#### Explanation:

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

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

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

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

•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)

$\text{let "(x_1,y_1)=(9,8)" and } \left({x}_{2} , {y}_{2}\right) = \left(4 , 7\right)$

$m = \frac{7 - 8}{4 - 9} = \frac{- 1}{- 5} = \frac{1}{5}$

$y = \frac{1}{5} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(4,7)" then}$

$7 = \frac{4}{5} + b \Rightarrow b = \frac{35}{5} - \frac{4}{5} = \frac{31}{5}$

$y = \frac{1}{5} x + \frac{31}{5} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{multiply through by 5}$

$5 y = x + 31$

$x - 5 y = - 31 \leftarrow \textcolor{red}{\text{in standard form}}$