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Line $v$ has a slope of $\frac{7}{9}$ . Line $w$ is perpendicular to $v$ . What is the slope of line $w$ ? $\newline$ 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

v

has a slope of

\frac{7}{9}

. Line

w

is perpendicular to

v

. What is the slope of line

w

?

\newline

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

\newline

\_\_

Identify Line Relationship: Line $w$ is perpendicular to $v$ , so their slopes are opposite reciprocals.
Find Slope of Line $v$ : Slope of line $v$ : $\frac{7}{9}$ . To find the slope of line $w$ , take the reciprocal of $\frac{7}{9}$ , which is $\frac{9}{7}$ .
Calculate Slope of Line $w$ : Now, since the slopes of perpendicular lines are not just reciprocals but also opposite in sign, change the sign of $\frac{9}{7}$ to get the slope of line $w$ . So, the slope of line $w$ is $-\frac{9}{7}$ .

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Question

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