Final answer:
The equation representing the line that passes through the points (2, -6) and (-4, 3) is y = -3/2x - 3, which is option D.
Step-by-step explanation:
To find which equation represents the line that passes through the points (2, -6) and (-4, 3), we first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Plugging in the given points, we get:
m = (3 - (-6)) / (-4 - 2) = 9 / -6 = -3/2.
Now, knowing the slope is -3/2, we use one of the points to find the y-intercept (b). Let's use (2, -6):
-6 = (-3/2)(2) + b
b = -6 + 3 = -3.
Therefore, the equation of the line is y = -3/2x - 3, which matches option D. This line has a slope of -3/2 and a y-intercept of -3. None of the other options match these criteria.