The problem states that a line $l$ has a slope $m = -\frac{2}{3}$. We are asked to find the slope of a line that is perpendicular to $l$.

1. Problem Description

The problem states that a line $l$ has a slope $m = -\frac{2}{3}$. We are asked to find the slope of a line that is perpendicular to $l$.

2. Solution Steps

If two lines are perpendicular, the product of their slopes is $-1$.

Let $m_1$ be the slope of line $l$ and $m_2$ be the slope of a line perpendicular to $l$.

Then $m_1 \cdot m_2 = -1$.

We are given that $m_1 = -\frac{2}{3}$. So,

$-\frac{2}{3} \cdot m_2 = -1$

$m_2 = -1 \cdot (-\frac{3}{2})$

$m_2 = \frac{3}{2}$

3. Final Answer

The slope of a line perpendicular to $l$ is $\frac{3}{2}$. The answer is b).