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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!

Find the slope of a line parallel to the line whose equation is 3x + 4y = 36. Fully simplify your answer.

Solve the linear equation 3x + 4y = 36 to find the slope of a line parallel to it. This problem focuses on rewriting equations in slope-intercept form and understanding the properties of parallel lines. Ideal for students in Grades 8-10.

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