Final answer:
The correct equation of the line passing through points (-3, 8), (0, 0), and (6, -16) is y = (-8/3)x, which doesn't match any of the provided options. There seems to be an error in the given choices.
Step-by-step explanation:
The equation of the line passing through the points –(-3, 8), (0, 0), and (6, -16)– can be found by calculating the slope of the line and using one of the points to find the y-intercept. First, let’s find the slope (m) using two of the points: m = (y2 - y1) / (x2 - x1). If we choose points (0, 0) and (6, -16), we get m = (-16 - 0) / (6 - 0) = -16/6 = -8/3. Next, using the slope and one of the points, we can plug into the point-slope form to get the full equation. Using the point (0, 0), which is the y-intercept (b), the equation becomes y = (-8/3)x + b, and since b is 0, the equation simplifies to y = (-8/3)x. This is not one of the options given, so we need to check if we've made a mistake or if there's a typo in the options.
Upon reviewing our calculation and the options offered, we find that there seems to be a mistake, as none of the provided options correspond to the slope we calculated. Since we are confident in our calculation, we may need to inform the student there might be an error in the question or the provided options.