Final answer:
To find the perpendicular line to the one passing through (-4, 2) and (4, -4), calculate the original line's slope, find the negative reciprocal for the perpendicular line's slope, and use a point from the original line to write the equation for the perpendicular line.
Step-by-step explanation:
To find a line perpendicular to the line passing through the points (-4, 2) and (4, -4), we first need to determine the slope of the given line. The slope (m) of a line that passes through two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1). In this case, the points are (-4, 2) and (4, -4), so the slope is m = (-4 - 2) / (4 - (-4)) = -6 / 8 = -3/4.
A line that is perpendicular to another has a slope that is the negative reciprocal of the original line's slope. Therefore, the slope of the perpendicular line we are looking for is the negative reciprocal of -3/4, which is 4/3.
Now that we have the slope of the perpendicular line, we need a point through which it passes to write its equation. We can choose either of the given points, for example, (-4, 2). Using the point-slope form of a line's equation, y - y1 = m(x - x1), we can plug in our slope 4/3 and the point (-4, 2) to get the equation of the line perpendicular to the original: y - 2 = (4/3)(x - (-4)) = (4/3)(x + 4).