Question

what is the slope of a line perpendicular to a line with a slope of -3?

a. 3

b. $\frac{1}{3}$

c. $-3$

d. $-\frac{1}{3}$

Explanation:

Step1: Recall the rule for perpendicular slopes

The slopes of two perpendicular lines are negative reciprocals of each other. That is, if a line has a slope \( m \), the slope of a line perpendicular to it, \( m_{\perp} \), is given by \( m_{\perp}=-\frac{1}{m} \).

Step2: Apply the rule to the given slope

We are given that the slope of the original line, \( m = - 3 \). To find the slope of the line perpendicular to it, we substitute \( m=-3 \) into the formula for the negative reciprocal.

First, find the reciprocal of \( - 3 \). The reciprocal of a number \( a \) is \( \frac{1}{a} \), so the reciprocal of \( - 3 \) is \( \frac{1}{-3}=-\frac{1}{3} \).

Then, take the negative of that reciprocal. The negative of \( -\frac{1}{3} \) is \( - (-\frac{1}{3})=\frac{1}{3} \).

Answer:

b. \(\frac{1}{3}\)