# How do you write the equation in point slope form given (–2, 4) and is perpendicular to the line y = –2x + 4?

Apr 30, 2017

Use ${m}_{p} = - \frac{1}{m}$ to find the slope of a perpendicular line
Use the point-slope form of the equation of a line to write the equation.

#### Explanation:

The slope of the line perpendicular to a line of the form $y = m x + b$ is:

${m}_{p} = - \frac{1}{m}$

The slope of any line perpendicular to the given line is:

${m}_{p} = - \frac{1}{-} 2$

${m}_{p} = \frac{1}{2}$

Use the slope, ${m}_{p} = \frac{1}{2}$, the given point $\left(- 2 , 4\right)$, and the point-slope form of a line, $y = m \left(x - {x}_{0}\right) + {y}_{0}$ to write the equation of the line:

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