# How do you find the equation of the line that passes through the point (1, -5). and is perpendicular to the line y=-1/2x+4?

Dec 26, 2016

The required equation is $y = 2 x - 7$

#### Explanation:

Given -

$y = - \frac{1}{2} x + 4$

Slope of the given line ${m}_{1} = - \frac{1}{2}$

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

${m}_{2} = - 1 \times \left(- \frac{2}{1}\right) = 2$

Then -

Let the equation of the required line be -

$y = m x + c$

Given the point $\left(1 , - 5\right)$ we have to find the value of $c$

$2 \times 1 + c = - 5$
$c = - 5 - 2 = - 7$

The required equation is $y = 2 x - 7$