Final answer:
To determine which line is perpendicular to the given line passing through the points (-4, 2) and (4, -4), we need to find the slope of the given line and the negative reciprocal of that slope. By comparing the slopes of the options, we can determine that the line represented by the equation 4x - 3y = 9 (Option D) is perpendicular.
Step-by-step explanation:
To determine which line is perpendicular to the line passing through the points (-4, 2) and (4, -4), we need to find the slope of the given line first. The slope of a line passing through two points can be found using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the given coordinates, we get m = (-4 - 2) / (4 - (-4)) = -6/8 = -3/4. The slope of a line perpendicular to a given line is the negative reciprocal of the given line's slope. So, the slope of the perpendicular line is -1/(-3/4) = 4/3.
Now, we can examine the options. We want to find a line with a slope of 4/3. By comparing the slopes of the options, we can determine which line is perpendicular:
- Option A: The slope is 3/4, not the negative reciprocal. Not perpendicular.
- Option B: The slope is -3/4, not the negative reciprocal. Not perpendicular.
- Option C: The slope is -4/3, not the negative reciprocal. Not perpendicular.
- Option D: The slope is 4/3. This line is perpendicular to the given line passing through the points (-4, 2) and (4, -4).
Therefore, the line perpendicular to the given line passing through the points (-4, 2) and (4, -4) is represented by the equation 4x - 3y = 9 (Option D).