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,
$\displaystyle (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 $\displaystyle \frac{2}{1}$ and change its sign.
Thus the perpendicular would have a slope of $\displaystyle -\frac{1}{2}$
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).
$\displaystyle y-y_1=m(x-x_1)$
$\displaystyle y-2=-\frac{1}{2}(x-4)$
That's it!