# What is the equation of the line with slope  m= 1/7  that passes through  (-3/11,2/3) ?

Dec 24, 2015

$231 y = 33 x + 163$

#### Explanation:

The general equation for a line is $y = m x + c$ where m is the slope and c is the y intercept. So $y = \left(\frac{1}{7}\right) x + c$
Substitute in the coordinates of the given point to find c
$\frac{2}{3} = \left(\frac{1}{7}\right) \left(- \frac{3}{11}\right) + c$
$c = \frac{2}{3} + \frac{3}{77}$
$c = \frac{2 \cdot 77 + 3 \cdot 3}{3 \cdot 77}$
$c = \frac{163}{231}$
$y = \left(\frac{1}{7}\right) x + \frac{163}{231}$ or $231 y = 33 x + 163$