Find the point on the line y = 5x + 9 that is closest to the origin.

Answer 1

Ok so you changed the slope.

Doesn't change how the problem is solved....

The distance function between the line and the origin is

D(x) = sqrt ( x^2 + 25x^2 + 90x+81)

= sqrt(26x^2 +90x+81)

Mminimizing, zero equals the derivative...

Derivative dD/Dx sends sqrt to the denominator...

Per chain rule, 52x+90 on top

Min occurs at -90/52=-45/26