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

Dec 8, 2015

$7 x + 17 y = - 31$

#### Explanation:

Using the general slope-point form for a line with slope $m$ through the point $\left(\hat{x} , \hat{y}\right)$
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

with the given values
$\textcolor{w h i t e}{\text{XXX}} \left(y + 1\right) = - \frac{7}{17} \left(x + 2\right)$

This could be simplified as:
$\textcolor{w h i t e}{\text{XXX}} 17 y + 17 = - 7 x - 14$

$\textcolor{w h i t e}{\text{XXX}} 7 x + 17 y = - 31$
(this is "standard form" for a linear equation)