The difference of the y-intercepts of the two linear functions is zero, as both functions have a y-intercept of 4.
To find the difference of the y-intercepts of the two linear functions, we first need to write both functions in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. For the first function defined by the equation 2x + 3y = 12, we can isolate y by subtracting 2x from both sides and then dividing by 3 to get y = -\(2/3\)x + 4, so the y-intercept (b) is 4.
For the second function passing through (3, -2) and (-2, 8), we first calculate the slope (m) which is (-2 - 8) / (3 - (-2)) = -10 / 5 = -2. With the slope, we can use one of the points to find the y-intercept (b) using the formula y = mx + b, leading to -2 = -2(3) + b, which simplifies to b = -2 + 6 = 4.
The y-intercept for both functions is 4, so the difference is 4 - 4 = 0. Therefore, the difference of the y-intercepts of the two functions is zero.