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)
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 and change its sign.
Thus the perpendicular would have a slope of
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).