To find the slope of a line parallel to the line given by the equation $3x + 3y = -36$, follow these steps:

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Step 1: Rewrite the equation in slope-intercept form.

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope.

Start with: $3x + 3y = -36$

Isolate $y$: $3y = -3x - 36$

Divide through by 3: $y = -x - 12$

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Step 2: Identify the slope.

From the equation $y = -x - 12$, the slope ($m$) is: $m = -1$

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Step 3: Find the slope of a parallel line.

Lines that are parallel have the same slope. Therefore, the slope of any line parallel to this one is: $\boxed{-1}$

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Final Answer:

The slope of a line parallel to the given line is: $\boxed{-1}$

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Would you like a breakdown of why parallel lines have the same slope or have additional questions? Here are 5 questions to further explore:

1. How can you find the slope of a line given two points?
2. What is the slope of a line perpendicular to $y = -x - 12$?
3. How do you convert between standard form and slope-intercept form?
4. What is the geometric significance of parallel lines in a coordinate plane?
5. How does the slope relate to the angle of inclination of a line?

Tip:

When converting an equation to slope-intercept form, always isolate $y$ to clearly see the slope.