# What is the equation of the line with slope  m= -7/17  that passes through  (2,1) ?

##### 1 Answer
Jun 25, 2016

$7 x + 17 y = 31$

#### Explanation:

In slope-point form:
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{red}{y '} = \textcolor{g r e e n}{m} \left(x - \textcolor{b l u e}{x '}\right)$
for a line with slope $\textcolor{g r e e n}{m}$ through the point $\left(\textcolor{b l u e}{x '} , \textcolor{red}{y '}\right)$

GIven $\textcolor{g r e e n}{m = - \frac{7}{17}}$ and the point $\left(\textcolor{b l u e}{x '} , \textcolor{red}{y '}\right) = \left(\textcolor{b u e}{2} , \textcolor{red}{1}\right)$

$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{red}{1} = \textcolor{g r e e n}{- \frac{7}{17}} \left(x - \textcolor{b l u e}{2}\right)$

Converting to standard form:
$\textcolor{w h i t e}{\text{XXX}} 17 y - 17 = - 7 x + 14$

$\textcolor{w h i t e}{\text{XXX}} 7 x + 17 y = 31$