# What is the equation of the line that passes through (-4,1) and is perpendicular to the line that passes through the following points: (3,-3,),(1,-4) ?

Mar 19, 2016

$y = - 2 x - 7$

#### Explanation:

First, get the slope $m '$ of the line that the line in question is perpendicular to.

$m ' = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}$

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

$\implies m ' = - \frac{1}{-} 2 = \frac{1}{2}$

Next, to get the slope $m$ of the desired line, we get the negative reciprocal of the slope $m '$ of the line is the perpendicular with

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

$\implies m = - \frac{1}{\frac{1}{2}} = - 2$

Now that we have the slope $m$ of the desired line, we must get the $y$-intercept of the line. We do this by substituting the coordinates of the point where we know the line passes through

$y = m x + b$
$\implies y = - 2 x + b$

$\implies 1 = - 2 \left(- 4\right) + b$

$\implies 1 = 8 + b$
$\implies b = - 7$

Hence, the equation of the line is

$y = - 2 x - 7$