# What is the equation of the line perpendicular to y=13x  that passes through  (7,8) ?

$y = - \frac{1}{13} x + 111$
Since the line is perpendicular to another line with slope $13$, its slope will be $13$'s opposite reciprocal, or $- \frac{1}{13}$. So the line we are trying to find has the equation $y = - \frac{1}{13} x + b$. Since it passes through $\left(7 , 8\right)$, it holds that $8 = - \frac{7}{13} + b \implies b = 111$.
So the final equation is $y = - \frac{1}{13} x + 111$