Answer:
y = x - 4
Step-by-Step Explanation:
Perpendicular lines have slopes that are negative reciprocals—multiplying their slopes result in -1.
Given the slope of a line m = -1, then it means that the slope of the other line must be 1 (because multiplying the slope of line 1 (m1 = -1), and the slope of the other line (m2 = 1) results in: -1 × 1 = -1).
Therefore, given the slope of line 2 (m2 = 1), and the point (2, -2), we could plug these values into the slope-intercept form and solve for the y-intercept (b):
y = mx + b
-2 = 1(2) + b
-2 = 2 + b
Subtract 2 from both sides to solve for b:
-2 - 2 = 2 - 2 + b
-4 = b
Therefore, the y-intercept (b) = -4.
Hence, the equation of the perpendicular line is: y = x - 4
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