First, we need to find the slope of the line that has an x-intercept of 4 and a y-intercept of -12. We can start by setting up the equation of the line using the intercepts:
y = mx + b
where m is the slope and b is the y-intercept. We know that the y-intercept is -12, so we can plug that in:
y = mx - 12
To find the slope, we can use the fact that the line passes through the two intercepts. The x-intercept is (4, 0), so the point-slope form of the equation would be:
y - 0 = m(x - 4)
Simplifying this gives:
y = mx - 4m
Now we can set this equal to the y-intercept and solve for the slope:
-12 = 4m
m = -3
So the slope of the line is -3. Since we want the line perpendicular to this one, we know that the slope of our function must be the negative reciprocal of -3, which is 1/3.
Now we can use the point-slope form of the equation to find the equation of our function, using the point (-9, 9):
y - 9 = (1/3)(x + 9)
Simplifying this gives:
y = (1/3)x + 12
So the slope-intercept equation of the function is y = (1/3)x + 12.