Final answer:
The equation that represents the direct variation function containing the points (-9, -3) and (-12, -4) is y = -x/3.
Step-by-step explanation:
The equation that represents the direct variation function containing the points (-9, -3) and (-12, -4) is y = -x/3.
To find the equation, we need to use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. First, we find the slope by using the formula m = (y2 - y1) / (x2 - x1). Substituting the given values, we get m = (-4 - (-3)) / (-12 - (-9)) = -1 / -3 = 1/3. Next, we choose one of the given points to find the y-intercept. Using (-12, -4), we substitute the values into the equation and solve for b. -4 = (1/3)(-12) + b. Solving for b, we get b = -4 + 4 = 0. Therefore, the equation is y = (1/3)x. Simplifying it, we have y = -x/3.