# Math Help - Help with Perpendicular Lines

1. ## Help with Perpendicular Lines

Find the equation for the line that is perpendicular to the line with the equation (y-1)=2(x-4) passing through the point (4,2)

2. Originally Posted by candygirl04
Find the equation for the line that is perpendicular to the line with the equation (y-1)=2(x-4) passing through the point (4,2)
Hi candygirl04,

$(y-1)=2(x-4)$ has a slope of 2. Did you know that?

The slope of any line perpendicular to that line will have a slope that is the negative reciprocal of 2. In other words invert $\frac{2}{1}$ and change its sign.

Thus the perpendicular would have a slope of $-\frac{1}{2}$

You didn't say which form of the linear equation to use, so I'll use the point slope form with our new slope and point (4, 2).

$y-y_1=m(x-x_1)$

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

That's it!