# What is the equation of the line perpendicular to y=6/7x  that passes through  (1,-3) ?

May 24, 2016

$y = - \frac{7}{6} x - \frac{11}{6}$

#### Explanation:

Given -

$y = \frac{6}{7} x$
Slope of the given line ${m}_{1} = \frac{6}{7}$

Two lines are perpendicular if -

${m}_{1} \times {m}_{2} = - 1$

${m}_{2}$ is the slope of the required line.

$\frac{6}{7} \times {m}_{2} = - 1$
${m}_{2} = - 1 \times \frac{7}{6} = - \frac{7}{6}$

Equation of the perpendicular line -

$y = m x + c$
$- 3 = - \frac{7}{6} \left(1\right) + c$
$c - \frac{7}{6} = - 3$
$c = - 3 + \frac{7}{6} = \frac{- 18 + 7}{6} = - \frac{11}{6}$

$y = - \frac{7}{6} x - \frac{11}{6}$