Calculus
posted by Morgan on .
Find the point on the line 4x+3y4=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
y2 = 3/4 (x5)
y = 3/4 x  7/4
These two lines intersect at (37/25,16/25) 
Thank you for your help!