Final answer:
The equation representing the direct variation function with the given points (-8, -6) and (12, 9) is y = (3/4)x.
Step-by-step explanation:
To find the equation representing the direct variation function that contains the points (-8, -6) and (12, 9), we first establish the formula for direct variation, which is y = kx, where k is the constant of variation.
We can find k by using either of the given points. Let's use (12, 9):
9 = k(12) => k = 9/12 => k = 3/4.
Thus, the equation of the direct variation function is:
y = (3/4)x.