The problem is asking to find the slope of a line parallel to the given line equation $2x - 3y = -18$. We need to express this equation in slope-intercept form, $y = mx + b$, where $m$ is the slope.

Let's solve the equation for $y$:

Starting with the original equation: $2x - 3y = -18$ We isolate $y$: $-3y = -2x - 18$ Divide both sides by $-3$: $y = \frac{2}{3}x + 6$

Thus, the slope $m$ of the given line is $\frac{2}{3}$.

Since parallel lines have the same slope, the slope of any line parallel to this one is also $\frac{2}{3}$.

Would you like further clarification or details?

Here are some related questions to consider:

1. How do you find the slope of a line from a general linear equation?
2. What is the significance of the slope for parallel lines?
3. How would you find the slope of a line perpendicular to this one?
4. Can you find the equation of a line parallel to this one that passes through a specific point?
5. How can slope be interpreted graphically?

Tip: Always rewrite a linear equation in slope-intercept form to easily identify its slope.