Question

question 9 of 10
lines a and b are perpendicular. if the slope of line a is 3, what is the slope of line b?
a. $\frac{1}{3}$
b. -3
c. $-\frac{1}{3}$
d. 3

Explanation:

Step1: Recall slope - perpendicularity rule

$m_1\times m_2=-1$ for perpendicular lines.

Step2: Assume slope of one line

Let $m_a = 3$ (arbitrary for illustration if not given).

Step3: Solve for the other slope

$3\times m_b=-1$, so $m_b=-\frac{1}{3}$.

Answer:

Let the slope of line $a$ be $m_a$ and the slope of line $b$ be $m_b$. For two perpendicular lines, the product of their slopes is - 1, i.e., $m_a\times m_b=-1$. If we assume the slope of line $a$ is 3 (since the question seems incomplete and we need a value to work with, and if we consider the relationship in general terms), then $3\times m_b=-1$. Solving for $m_b$, we get $m_b =-\frac{1}{3}$. So the answer is C. $-\frac{1}{3}$.