Question

Write the equation of the line in slope intercept that is perpendicular to the given line and goes through the given point y=1/2x+2; (4,2)

Answer 1

The product of the slopes of 2 perpendicular lines is equal to -1. It means:

$m1\cdot m2=-1$

The given equation has a slope of 1/2, use this value to find the slope of the line perpendicular to it.

$\begin{gathered} \frac{1}{2}\cdot m2=-1 \\ m2=-1\cdot\frac{2}{1} \\ m2=-2 \end{gathered}$

Using this slope and the given point, find the slope intercept equation by replacing the values in the slope point form:

$\begin{gathered} y-2=-2(x-4) \\ y-2=-2x+8 \\ y=-2x+8+2 \\ y=-2x+10 \end{gathered}$

The equation in slope intercept form is y = -2x + 10.