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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.

Find the slope of a line parallel to the line whose equation is 2x - 3y = -18. Fully simplify your answer.

Learn how to find the slope of a line parallel to 2x - 3y = -18 by converting it to slope-intercept form. Understand key concepts in algebra and linear equations, suitable for Grades 8-10.

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