To find the point of intersection for f(x) and g(x), you can sent them equal to each other to find x.
f(x) = g(x)
-5x + 12 = -2x - 3
-3x = -15
x = -15/-3
x = 5
Now that you have x, you can plug it into either f(x) or g(x) to get y. (You get the same y value)
f(x) = -5(5) + 12
f(x) = -25 + 12
f(x) = -13
g(x) = -2(5) - 3
g(x) = -10 - 3
g(x) = -13
The point of intersection is (5, -13)
