Question

line a has a slope of \\(\frac{-5}{3}\\). line b is perpendicular to a. what is the slope of line b? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall perpendicular slope rule

For two perpendicular lines, the product of their slopes is -1. If slope of line \(a\) is \(m_1\) and slope of line \(b\) is \(m_2\), then \(m_1\times m_2=-1\).

Step2: Substitute \(m_1 = \frac{-5}{3}\)

We have \(\frac{-5}{3}\times m_2=-1\). Solve for \(m_2\) by dividing both sides by \(\frac{-5}{3}\), which is equivalent to multiplying by \(\frac{-3}{5}\). So \(m_2=-1\times\frac{-3}{5}=\frac{3}{5}\).

Answer:

\(\frac{3}{5}\)