Final answer:
The equation of the direct variation function that passes through the points (-8, -6) and (12, 9) is y = (3/4)x, found by determining the constant of variation k from the given points.
Step-by-step explanation:
The student is asking to find the equation of a direct variation function that passes through the points (–8, –6) and (12, 9). A direct variation function has the form y = kx, where k is the constant of variation. To find the value of k, we use the given points.
Using the point (–8, –6), we get:
–6 = k(–8)
k = 6/8
k = 3/4
Using the point (12, 9), we get:
9 = k(12)
k = 9/12
k = 3/4
Both points yield the same constant of variation, k = 3/4. Therefore, the equation of the direct variation function is y = (3/4)x.