# What is the equation of the line with slope  m= -18/49  that passes through  (4/7, 17/21) ?

Apr 20, 2016

$378 x + 1029 y = 1049$

#### Explanation:

Since the slope $m$ is defined as
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\Delta y}{\Delta x}$

$m = - \frac{18}{49} = \frac{y - \frac{17}{21}}{x - \frac{4}{7}}$

After multiplying the right side by $\frac{21}{21}$
$\textcolor{w h i t e}{\text{XXX}} - \frac{18}{49} = \frac{21 y - 17}{21 x - 12}$

Cross multiplying
$\textcolor{w h i t e}{\text{XXX}} \left(18\right) \left(12 - 21 x\right) = 49 \left(21 y - 17\right)$

Simplifying:
$\textcolor{w h i t e}{\text{XXX}} 216 - 378 x = 1029 y - 833$

$\textcolor{w h i t e}{\text{XXX}} 378 x + 1029 y = 1049$