Final answer:
The slope for a line that is perpendicular to the line passing through (1, -1) and (-5, 3) is 3/2.
Step-by-step explanation:
The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the slope of the given line.
First, let's find the slope of the given line using the formula:
slope = (y2 - y1) / (x2 - x1)
By substituting the coordinates (1, -1) and (-5, 3) into the formula, we get:
slope = (3 - (-1)) / (-5 - 1) = 4 / -6 = -2/3
Since the slope of the given line is -2/3, the slope of the line perpendicular to it would be the negative reciprocal:
slope of perpendicular line = -1 / (-2/3) = 3/2
Therefore, the slope for a line that is perpendicular to the line passing through (1, -1) and (-5, 3) is 3/2.