# What is the equation of the line perpendicular to y=-1/5x  that passes through  (7,4) ?

May 17, 2017

$y = 5 x - 31$

#### Explanation:

Given -

$y = - \frac{1}{5} x$

Slope of the given line

${m}_{1} = - \frac{1}{5}$

The two line are perpendicular

Slope of the second line ${m}_{2} = \frac{1}{{m}_{1}} \times - 1 = - 5 \times - 1 = 5$

Second line passes through the point $\left(7 , 4\right)$

Equation of the second line

$y = m x + c$
$4 = \left(5 \times 7\right) + c$
$4 = 35 + c$

$c = 4 - 35 = - 31$

$y = 5 x - 31$