# How do you write an equation of a line perpendicular to y= 3/4x - 2 and passes through (-12,7)?

Nov 1, 2015

$y = - \frac{4}{3} x - 9$

#### Explanation:

First we need to get the slope of the perpendicular line

The slope of a perpendicular line is equal to the negative inverse of the slope of the given line

$y = m x + b$

$y = \frac{3}{4} x - 2$

$\implies m = \frac{3}{4}$

$m ' = - \frac{1}{m}$

$\implies m ' = - \frac{1}{\frac{3}{4}}$

$\implies m ' = - \frac{4}{3}$

Now that we have the slope, we need to find the y-intercept.
To find the y-intercept, we need to plug-in values of $x$ and $y$ that the line passes through

$y ' = m ' x ' + b$

$\implies y ' = - \frac{4}{3} x ' + b$

$\implies 7 = - \frac{4}{3} \left(- 12\right) + b$

$\implies 7 = 16 + b$

$\implies b = - 9$

Therefore, the equation of the line is

$y = - \frac{4}{3} x - 9$