# How do you find a standard form equation for the line with P (2, 4) and is perpendicular to the line y = -2x + 12?

Oct 22, 2017

Standard form of equation for the perpendicular line is
$y = \left(\frac{1}{2}\right) x + 3$

#### Explanation:

Standard form of equation is
$y = m x + c$ where m is the slope.

$y = - 2 x + 12$
Slope m1 = -2#

Slope of perpendicular line $m 2 = - \left(\frac{1}{m} 1\right) = - \left(\frac{1}{-} 2\right) = \frac{1}{2}$

Equation of perpendicular line passing through point P (2,4) is
$y - {y}_{P} = {m}_{2} \left(x - {x}_{P}\right)$

$\left(y - 4\right) = \left(\frac{1}{2}\right) \left(x - 2\right)$

$y = \left(\frac{1}{2}\right) \left(x - 2\right) + 4$

$y = \left(\frac{1}{2}\right) \left(x\right) - 1 + 4 = \left(\frac{1}{2}\right) x + 3$