Question 1119703
The equation of the line may be rewritten as y=2x+2 and has slope 2
The line perpendicular to it has slope -1/2, the negative reciprocal.
y-y1=m(x-x1) point slope formula where m is slope and (x1, y1) point
y-4=(-1/2)(x-3)
y=-x/2 + 11/2
{{{graph(300,300,-10,10,-10,10,2x+2,(-x/2)+(11/2))}}}

This is (x^2+2xh+h^2+4x+4h-5-(x^2+4x-5) divided by h
The numerator becomes 2xh+h^2+4h, the denominator h
This simplifies to 2x+h+4 and as h goes to 0, that becomes 2x+4, which is the derivative

f(x+h) for the function is (x+h)^2+4(x+h)-5, which is where the numerator came from.