Question

What is the slope of a line perpendicular to the line whose equation is 3 x + y = − 9 3x+y=−9.

Answer 1

Answer: 1/3

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Step-by-step explanation:

The equation Ax+By = C has the slope m = -A/B

In the equation 3x+y = -9, we have

• A = 3
• B = 1
• C = -9

The first two values give us a slope of m = -A/B = -3/1 = -3

The negative reciprocal of this is 1/3 which is the perpendicular slope. We flip the fraction and flip the sign.

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Extra info:

• The original slope -3 and perpendicular slope 1/3 multiply to -1. This is true of any pair of perpendicular lines where neither is vertical nor horizontal.
• If given Ax+By = C, then Bx-Ay = D is perpendicular to that given equation.
• Based on the 2nd fact, the given equation 3x+y = -9 has x-3y = D perpendicular to it, where D is any real number.