# What is the equation of the line perpendicular to y=-7/9x  that passes through  (5,1) ?

Feb 9, 2016

9x−7y=38

#### Explanation:

Product of slope of two perpendicular lines is always $- 1$. As the equation is in slope-intercept form, its slope is $- \frac{7}{9}$ and hence slope of perpendicular line will be $\frac{9}{7}$. Hence equation will be

$y = \left(\frac{9}{7}\right) \cdot x + c$

Putting $x = 5$ and $y = 1$, this becomes

$1 = \left(\frac{9}{7}\right) \cdot 5 + c$ or $c = 1 - \left(\frac{45}{7}\right)$

i.e. $c = - \frac{38}{7}$

Hence equation is $y = \left(\frac{9}{7}\right) \cdot x - \frac{38}{7}$ which can be simplified to

$9 x - 7 y = 38$