Question

lines a and b are perpendicular. if the slope of line a is 3, what is the slope of line b?

a. 3

b. -3

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

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

Explanation:

Step1: Recall the rule for perpendicular lines

For two perpendicular lines with slopes \(m_1\) and \(m_2\), the product of their slopes is \(- 1\), i.e., \(m_1\times m_2=-1\).

Step2: Substitute the given slope

Let the slope of line \(a\) be \(m_1 = 3\) and the slope of line \(b\) be \(m_2\). Using the formula \(m_1\times m_2=-1\), we substitute \(m_1 = 3\) into it: \(3\times m_2=-1\).

Step3: Solve for \(m_2\)

To find \(m_2\), we divide both sides of the equation \(3\times m_2=-1\) by \(3\). So \(m_2=\frac{- 1}{3}=-\frac{1}{3}\).

Answer:

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