QuestionThe equation of line $a$ is $y=\frac{-8}{3} x+\frac{9}{8}$. 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.

Studdy Solution
Calculate the slope of line $b$.
Using the relationship $m_a \times m_b = -1$, substitute $m_a = \frac{-8}{3}$:
$$\frac{-8}{3} \times m_b = -1$$
To find $m_b$, divide both sides by $\frac{-8}{3}$:
$$m_b = \frac{-1}{\frac{-8}{3}}$$
Simplify the expression by multiplying by the reciprocal:
$$m_b = \frac{-1 \times 3}{-8}$$
$$m_b = \frac{3}{8}$$
The slope of line $b$ is:
$$\boxed{\frac{3}{8}}$$