Line e has a slope of 2/3 .Line f is perpendicular to e.What is the slope of line f? Simplify your answer and write it as a proper fraction, improper fraction, or integer. _____

Identify Perpendicular Lines: Line f is perpendicular to e, so their slopes are opposite reciprocals.Find Slope of Line e: Slope of line e: 2/3. To find the slope of line f, take the reciprocal of 2/3, which is 3/2.Calculate Opposite Reciprocal: Now, since the slopes of perpendicular lines are not just reciprocals but opposite reciprocals, we need to take the opposite of 3/2. The opposite of 3/2 is -3/2.Determine Slope of Line f: So, the slope of line f is -3/2.

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Line $e$ has a slope of $\frac{2}{3}$ . Line $f$ is perpendicular to $e$ . What is the slope of line $f$ ?

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Algebra 1

Slopes of parallel and perpendicular lines

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Q. Line

e

has a slope of

\frac{2}{3}

. Line

f

is perpendicular to

e

. What is the slope of line

f

Identify Perpendicular Lines: Line $f$ is perpendicular to $e$ , so their slopes are opposite reciprocals.
Find Slope of Line e: Slope of line $e$ : $\frac{2}{3}$ . $\newline$ To find the slope of line $f$ , take the reciprocal of $\frac{2}{3}$ , which is $\frac{3}{2}$ .
Calculate Opposite Reciprocal: Now, since the slopes of perpendicular lines are not just reciprocals but opposite reciprocals, we need to take the opposite of $\frac{3}{2}$ . The opposite of $\frac{3}{2}$ is $-\frac{3}{2}$ .
Determine Slope of Line $f$ : So, the slope of line $f$ is $-\frac{3}{2}$ .