What is the equation of the line with slope  m= -5/6  that passes through  (-5/12,4/3) ?

Dec 1, 2015

$60 x + 72 y = 71$

Explanation:

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

we can insert the given values $m = \left(- \frac{5}{6}\right)$ and $\left(\hat{x} , \hat{y}\right) = \left(- \frac{5}{12} , \frac{4}{3}\right)$
to get
$\textcolor{w h i t e}{\text{XXX}} \left(y - \frac{4}{3}\right) = \left(- \frac{5}{6}\right) \left(x + \frac{5}{12}\right)$

Theoretically we could claim that this is the answer but it's ugly, so let's convert it into "standard form" ($A x + B y = C$)

We can see by looking at the right side that to clear the denominators we will need to multiply both sides by $72$ (i.e. $6 \times 12$)
$\textcolor{w h i t e}{\text{XXX}} 72 y - 96 = - 60 x - 25$

Adding $60 x + 96$ to both sides to shift the $x$ term to the left side and the constant to the right:
$\textcolor{w h i t e}{\text{XXX}} 60 x + 72 y = 71$