This problem is an applied optimization problem. The problem is to minimize
the area of the triangle formed by a tangent line to the function y = 1⁄9 x2.
The triangle is defined by the origin, the x-intercept of the tangent line, and the
y-intercept of the tangent line. Only triangles formed in the first quadrant are
of concern.
In this note, we will show how transformations can be used to obtain a radically simple derivation of the equation of the line of best fit. Our approach also gives a simple geometric interpretation of the Pearson correlation coefficient.