Question

given a line has a slope of $-\frac{3}{4}$, what is the slope of a line perpendicular to it? options: $\frac{3}{4}$, $\frac{4}{3}$, $-\frac{4}{3}$

Explanation:

Step1: Recall the rule for perpendicular slopes

The slopes of two perpendicular lines are negative reciprocals of each other. That is, if the slope of one line is \( m \), the slope of the line perpendicular to it is \( -\frac{1}{m} \).

Step2: Apply the rule to the given slope

Given the slope of the line is \( -\frac{3}{4} \). Let the slope of the perpendicular line be \( m_{\perp} \).
First, find the reciprocal of \( -\frac{3}{4} \), which is \( -\frac{4}{3} \). Then, take the negative of that reciprocal. The negative of \( -\frac{4}{3} \) is \( \frac{4}{3} \).

Answer:

\(\frac{4}{3}\) (corresponding to the middle option)