The y-intercept is the y-coordinate of the point that has zero as its x-coordinate.
First, we find the y-intercept of function f.
f(x) = 3x - 9
Let x = 0, and solve for f(0).
f(0) = 3(0) - 9
f(0) = -9
The y-intercept of function f is -9.
Now we find the y-intercept of function g.
We are told that both functions are linear, so equal changes in x produce equal changes in y. Look at these two points in function g: (3, 10) and (4, 14).
As x goes from 4 to 3, y goes from 14 to 10. When x is 1 less than it was, the corresponding y is 4 less than it was. That allows us to find the y-coordinate when x = 0. When x = 1, y = 2. By subtracting 1 from x, you must subtract 4 from y, so when x = 0, y = -2. That gives us point (0, -2). The y-intercept of function g is -2.
Now we subtract the y-intercept of f(x) from the y-intercept of g(x).
g(0) - f(0) = -9 - (-2) = -9 + 2 = -7
Answer: -7
