What is the slope of a line perpendicular to the line whose equation is x - 3y = -18. Fully reduce your answer.

Question
Functions
asked 2021-01-05
What is the slope of a line perpendicular to the line whose equation is x - 3y = -18. Fully reduce your answer.

Answers (1)

2021-01-06
Perpendicular lines have slopes that are negative reciprocals. First, we write the given equation in slope intercept form by solving for y:
x-3y=-18
-3y=-x-18
\(\displaystyle{y}=\frac{{-{x}-{18}}}{{-{{3}}}}\)
\(\displaystyle{y}=\frac{{1}}{{3}}{x}+{6}\)
So, the slope of the given line is \(\displaystyle\frac{{1}}{{3}}\) which means that the slope of the line perpendicular to it is:
\(\displaystyle-\frac{{\frac{{1}}{{1}}}}{{3}}=-{3}\)
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