# How do you write the equation of a line that is perpendicular to the given line and that passes through the given point: y-4=5/2(x+3); (-7,8)?

Jun 13, 2018

$y = - \frac{2}{5} x + \frac{26}{5}$

#### Explanation:

$y - 4 = \frac{5}{2} \left(x + 3\right)$

$2 y - 8 = 5 x + 15$

$2 y = 5 x + 23$

$y = \frac{5}{2} x + \frac{23}{2}$

if it is perpendicular then when you multiply the gradients together you get -1

so the gradient of the new line is $- \frac{2}{5}$

The line is of the form $y = - \frac{2}{5} x + c$ but we know it passes through (-7,8) so if we put these values in we will get the equation.

$8 = - \frac{2}{5} \times - 7 + c$

$8 = \frac{14}{5} + c$

$c = 5 \frac{1}{5}$