Find the point on the line 5x+4y−2=0 which is closest to the point (−6,−7).

Answer 1

Hardly a calculus question.

The closet point is on the perpendicular to the line of 5x + 4y - 2 = 0 and passing through (-6, -7)

Determine slope of 5x + 4y - 2 = 0

Make negative reciprocal of slope the slope, m, in

y + 7 = m(x + 6)

Determine intersection of above equation and the original equation.