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The given equation is:

\[
3y - 3x = -27
\]

We need to convert this into the slope-intercept form, which is:

\[
y = mx + b
\]

### Steps:

1. Start by isolating \(y\). First, add \(3x\) to both sides of the equation:

\[
3y = 3x - 27
\]

2. Next, divide the entire equation by 3 to solve for \(y\):

\[
y = x - 9
\]

So, the slope-intercept form of the equation is:

\[
y = x - 9
\]

### Simplified:
- Slope (\(m\)) = 1
- Intercept (\(b\)) = -9

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you find the slope and y-intercept from an equation in slope-intercept form?
2. What is the geometric meaning of the slope in a line equation?
3. How would the equation change if the slope was negative?
4. What steps would you take to convert a line equation from standard form to slope-intercept form?
5. Can you identify a real-world situation where knowing the slope of a line is useful?

**Tip:** In slope-intercept form, the coefficient of \(x\) represents the slope of the line, and the constant term is the y-intercept, where the line crosses the y-axis.

Put the following equation of a line into slope-intercept form, simplifying all fractions: 3y - 3x = -27

Learn how to convert the equation 3y - 3x = -27 into slope-intercept form (y = mx + b). This example covers essential linear algebra concepts and provides a step-by-step solution. Suitable for students in Grades 7-10.

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