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Line $m$ has a slope of $\frac{3}{7}$ . Line $n$ is perpendicular to $m$ . What is the slope of line $n$ ? $\newline$ Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\newline$ $\_\_$

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Slopes of parallel and perpendicular lines

Full solution

Q. Line

m

has a slope of

\frac{3}{7}

. Line

n

is perpendicular to

m

. What is the slope of line

n

?

\newline

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

\newline

\_\_

Perpendicular Lines Relationship: Line $n$ is perpendicular to $m$ , so their slopes are opposite reciprocals.
Finding Slope of Line $m$ : Slope of line $m$ : $\frac{3}{7}$ $\newline$ To find the slope of line $n$ , take the reciprocal of $\frac{3}{7}$ , which is $\frac{7}{3}$ .
Reciprocal and Sign Change: Now, since line $n$ is perpendicular, we need the opposite sign. So if $m$ 's slope is positive, $n$ 's slope will be negative.
Slope of Line n: Therefore, the slope of line n is $-\frac{7}{3}$ .

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