For this case we must solve each of the functions.
We have then:
f (x) = x2 - 9, and g (x) = x - 3
h (x) = (x2 - 9) / (x - 3)
h (x) = ((x-3) (x + 3)) / (x - 3)
h (x) = x + 3
f (x) = x2 - 4x + 3, and g (x) = x - 3
h (x) = (x2 - 4x + 3) / (x - 3)
h (x) = ((x-3) (x-1)) / (x - 3)
h (x) = x-1
f (x) = x2 + 4x - 5, and g (x) = x - 1
h (x) = (x2 + 4x - 5) / (x - 1)
h (x) = ((x + 5) (x-1)) / (x - 1)
h (x) = x + 5
f (x) = x2 - 16, and g (x) = x - 4
h (x) = (x2 - 16) / (x - 4)
h (x) = ((x-4) (x + 4)) / (x - 4)
h (x) = x + 4
Hmm they're both even numbers so maybe we can start by cutting each number in half.

18 and 48 had 2 as a common factor.
So factoring a 2 out of each number was the same as cutting each number in half. Try to do something similar with the 9 and 24. They each have something in common.
Slope formular = (y2-y1)/(x2 - x1)
so
slope = (-6 +5)/(-4-3)
slope = -1/-7
slope = 1/7
answer
Laila is correct