Perpendicular lines have negative reciprocal slopes, in which the product of the slopes of both lines = -1.
Given the linear equation, y = -3x + 4 and the point, (-1, 6):
We can assume that the slope of the other line must be 1/3, because if you multiply 1/3 by -3, the product will be -1.
Substitute the values if the given point, (-1, 6) and the slope of the other line, m = 1/3 into the slope-intercept form to solve for the y-intercept (b) of the other line:
y = mx + b
6 = 1/3(-1) + b
6 = -1/3 + b
Add 1/3 to both sides
6 + 1/3 = -1/3 + 1/3 + b
19/3 = b
Therefore, given the slope of 1/3 and the y-intercept, b = 19/3, the equation of the other line is:
y = 1/3x + 19/3
Attached is a screenshot of the graph of both equations, proving that both lines are perpendicular from each other, and that y = 1/3x + 19/3 passes through point (-1, 6).
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