# What is the equation of the line with slope  m= 1/6  that passes through  (-5/12,4/3) ?

$12 x - 72 y + 101 = 0.$
If a line with slope $m$ passes thro. pt. $\left({x}_{1} , {y}_{1}\right)$, its eqn. is given by, : $y - {y}_{1} = m \left(x - {x}_{1}\right) .$
Using this, we can write the desired eqn. as $y - \frac{4}{3} = \frac{1}{6} \left(x + \frac{5}{12}\right) ,$ or, $\left(3 y - 4\right) = \frac{1}{2} \left(x + \frac{5}{12}\right) ,$ i.e., $24 \left(3 y - 4\right) = 12 x + 5.$
$\therefore 12 x + 5 - 72 y + 96 = 0 ,$ i.e., $12 x - 72 y + 101 = 0.$