Line q has a slope of 5/3 .Line r is perpendicular to q.What is the slope of line r? Simplify your answer and write it as a proper fraction, improper fraction, or integer. _____

Perpendicular Line Requirement: Line r is perpendicular to q, so we need the opposite reciprocal of q's slope Reciprocal of q's Slope: Slope of line q is 5/3, so the reciprocal is 3/5 Opposite of Reciprocal: Now we take the opposite of 3/5, which is -3/5 Slope of Line r: So the slope of line r is -3/5

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Line $q$ has a slope of $\frac{5}{3}$ . Line $r$ is perpendicular to $q$ . What is the slope of line $r$ ? $\newline$ Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\newline$ $\_\_\_\_\_$

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Math Problems

Algebra 1

Slopes of parallel and perpendicular lines

Full solution

Q. Line

q

has a slope of

\frac{5}{3}

. Line

r

is perpendicular to

q

. What is the slope of line

r

\newline

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

\newline

\_\_\_\_\_

Perpendicular Line Requirement: Line $r$ is perpendicular to $q$ , so we need the opposite reciprocal of $q$ 's slope
Reciprocal of q's Slope: Slope of line $q$ is $\frac{5}{3}$ , so the reciprocal is $\frac{3}{5}$
Opposite of Reciprocal: Now we take the opposite of $\frac{3}{5}$ , which is $-\frac{3}{5}$
Slope of Line r: So the slope of line r is $-\frac{3}{5}$