Find the point on the line y equals 4x plus 7 that is closest to the origin?

(28/17,7/17)

The point on the line closest to the origin is the point on a line through the origin that is perpendicular to the given line. Because the slope of the perpendicular is the negative reciprocal of the given line, it has a slope of -1/4 and is given by the equation:

y=(-1/4)x

The x-coordinate of the point of intersection is found by solving the following:

(-1/4)x=4x+7

-x=16x+28

-17x=28

x=-28/17

y=(-1/4)(-28/17)=7/17