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Line qq has a slope of 53\frac{5}{3}. Line rr is perpendicular to qq. What is the slope of line rr? \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 qq has a slope of 53\frac{5}{3}. Line rr is perpendicular to qq. What is the slope of line rr? \newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____\_\_\_\_\_
  1. Perpendicular Line Requirement: Line rr is perpendicular to qq, so we need the opposite reciprocal of qq's slope
  2. Reciprocal of q's Slope: Slope of line qq is 53\frac{5}{3}, so the reciprocal is 35\frac{3}{5}
  3. Opposite of Reciprocal: Now we take the opposite of 35\frac{3}{5}, which is −35-\frac{3}{5}
  4. Slope of Line r: So the slope of line r is −35-\frac{3}{5}

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