Question

Find the point on the line y = 4x + 3 that is closest to the origin.

Answer 1

That point will be where the perpendicular line through the origin intersects the given line.
.. (-1/4)x = 4x +3
.. -3 = (17/4)x
.. -12/17 = x

The point on the given line that is closest to the origin is (-12/17, 3/17).