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What is the slope intercept form of the equation of the line that is perpendicular to 7x - 8y equals 12 and contains the point P at -3 1?
Wiki User
∙ 6y ago
The slope m' of a line perpendicular to a line with slope m is such that m'm = -1 → m' = -1/m
A line with slope m' through point (X, Y) has equation: y - Y = m'(x - X)
→ The line perpendicular to 7x - 8y = 12 through p (-3, 1) is found:
7x - 8y = 12
→ 8y = 7x - 12
→ y = (7/8)x - 3/2
→ The slope of 7x - 8y = 12 is m = 7/8
→ The slope of the perpendicular line is m' = -1/m = -1/(7/8) = -8/7
→ The line through P with this slope m' is:
y - 1 = -8/7(x - -3)
→ y = (-8/7)x - 24/7 + 1
→ y = (-8/7)x - 17/7
This can be rearranged into:
y = (-8/7)x - 17/7
→ 7y = -8x - 17
→ 7y + 8x + 17 = 0
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∙ 6y ago
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