To find the slope of a line parallel to the given equation $3x + 4y = 36$, we need to rewrite this equation in slope-intercept form, $y = mx + b$, where $m$ represents the slope.

Steps:

1. Start with the given equation: $3x + 4y = 36$

2. Solve for $y$: $4y = -3x + 36$ $y = -\frac{3}{4}x + 9$

Now, we have the equation in slope-intercept form. The slope of this line is $m = -\frac{3}{4}$.

Parallel Lines:

Lines that are parallel have the same slope. Therefore, the slope of the line parallel to this one is also $m = -\frac{3}{4}$.

Let me know if you'd like further details or have any questions!

Related Questions:

1. How do you find the slope of a perpendicular line?
2. What are other ways to represent the equation of a line?
3. How do you convert a standard form equation to slope-intercept form?
4. Can two lines be parallel if their slopes are different?
5. What does the y-intercept of a line represent?

Tip: For parallel lines, always focus on the slope—it stays constant!