posted by Morgan .
Find the point on the line 4x+3y-4=0 which is closest to the point (5,2)
A line from (5,2) perpendicular to the curve will have the shortest distance to the curve.
The slope of the graph is -4/3, so the normal has slope 3/4
So, now you have a point and a slope, so the perpendicular line through (5,2) is
y-2 = 3/4 (x-5)
y = 3/4 x - 7/4
These two lines intersect at (37/25,-16/25)
Thank you for your help!