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Line q q has a slope of −23 \frac{-2}{3} . Line r r is perpendicular to q q . What is the slope of line r r ?\newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____\_\_\_\_\_

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Slopes of parallel and perpendicular linesright chevron icon

Full solution

Q. Line q q has a slope of −23 \frac{-2}{3} . Line r r is perpendicular to q q . What is the slope of line r r ?\newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____\_\_\_\_\_
  1. Find Reciprocal: Line qq's slope is −23-\frac{2}{3}. Perpendicular lines have slopes that are opposite reciprocals.
  2. Flip Slope: To find the reciprocal, flip the slope of line qq. So, the reciprocal of −23-\frac{2}{3} is −32-\frac{3}{2}.
  3. Get Opposite: Now, take the opposite of −32-\frac{3}{2} to get the slope of line rr. The opposite of −32-\frac{3}{2} is 32\frac{3}{2}.

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