Put the following equation of a line into slope-intercept form, simplifying all fractions.

3, y, minus, 3, x, equals, minus, 27

To put the equation \(3y - 3x = -27\) into slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:

1. **Add \(3x\) to both sides** to isolate the \(y\) term on the left side:
   \[
   3y = 3x - 27
   \]

2. **Divide the entire equation by 3** to solve for \(y\):
   \[
   \frac{3y}{3} = \frac{3x - 27}{3}
   \]
   Simplifying, you get:
   \[
   y = x - 9
   \]

So, the equation in slope-intercept form is:
\[
y = x - 9
\]
This equation shows that the slope (\(m\)) is 1, and the y-intercept (\(b\)) is \(-9\).

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. What is the slope of the line \( y = x - 9 \)?
2. How would you graph the line \( y = x - 9 \)?
3. If \( y = x - 9 \), what is the value of \( y \) when \( x = 5 \)?
4. How does the slope-intercept form compare to the standard form of a linear equation?
5. How would the line change if the equation was \( y = 2x - 9 \)?

**Tip:** The slope-intercept form is very useful for quickly identifying the slope and y-intercept of a line, which makes graphing the line much easier.

Learn how to convert the equation 3y - 3x = -27 into slope-intercept form (y = mx + b) with a detailed step-by-step solution. This problem covers linear equations and slope calculations. Suitable for students in Grades 7-9.

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