What is the equation of the line with slope  m= -7/6  that passes through  (-7/12,2/3) ?

Apr 12, 2016

$84 x + 72 y = - 1$

Explanation:

Using the definition of slope:
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\Delta y}{\Delta x}$
and given values:
$\textcolor{w h i t e}{\text{XXX}}$slope: $m = - \frac{7}{6}$,
$\textcolor{w h i t e}{\text{XXX}}$a point: $\left(- \frac{7}{12} , \frac{2}{3}\right)$,
and using a variable point $\left(x , y\right)$ on the required line:

$\textcolor{w h i t e}{\text{XXX}} - \frac{7}{6} = \frac{y - \frac{2}{3}}{x - \left(- \frac{7}{12}\right)}$

Multiplying the right side by $\frac{12}{12}$ to clear the fractions:
$\textcolor{w h i t e}{\text{XXX}} - \frac{7}{6} = \frac{12 y - 8}{12 x + 7}$

Then multiply both sides by $6 \left(12 x + 7\right)$ to clear the denominators
$\textcolor{w h i t e}{\text{XXX}} - 7 \left(12 x + 7\right) = 6 \left(12 y - 8\right)$

Simplify
$\textcolor{w h i t e}{\text{XXX}} - 84 x - 49 = 72 y - 48$

Add $\left(84 x + 48\right)$ to both sides (and flip the sides to write in standard form)
$\textcolor{w h i t e}{\text{XXX}} 84 x + 72 y = - 1$