# How do you write an equation of a line through (1, -3) and perpendicular to y=1/2x +4?

May 18, 2017

First find the slope

Slopes of perpendicular equations are the opposite reciprocals of the original slope

Original slope = $\frac{1}{2} x$

Perpendicular slope = $- 2 x$

$$  See how it is the reciprocal of the original slope and the opposite sign of the original slope.


Then plug in the points you want this line to pass through, in this case it is $\left(1 , - 3\right)$ in order to find the $b$ value

Rewrite equation in $y = m x + b$ format plugging in the values for $x$ and $y$ to find $b$

$- 3 = - 2 \cdot \left(1\right) + b$

Isolate the $b$ value

$- 1 = b$

The Perpendicular equation is:

$y = - 2 x - 1$