How do I use the limit process to find the slope of the graph of the function at the specified point

g(x)=x^2-4x, (3,-3)

lim h->3 [f(h)-f(3)]/(h-3)
=(h^2-4h+3)/(h-3)
=(h-1)(h-3)/(h-3)
=(h-1)
Let h=3 and get 2

slope at x = 3 is lim as x ==> 3 of [g(x) - g(3)] / (x - 3)
= lim x ==> 3 of [x^2 - 4x - (3^2 - 4(3))] / (x - 3)
= lim x ==> 3 of [x^2 - 4x + 3] / (x - 3)
= lim x ==> 3 of (x - 3)(x - 1) / (x - 3)
= lim x ==> 3 of x - 1
= 2

slope at x = 2 is 2

g'(x)=2x-4
g'(3)=2(3)-4=2

the slope is two (at x=3)