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

3x−3y=18

To convert the given equation \( 3x - 3y = 18 \) into slope-intercept form \( y = mx + b \), follow these steps:

1. **Isolate the \( y \)-term**:  
   Move \( 3x \) to the other side by subtracting it from both sides of the equation:
   \[
   -3y = -3x + 18
   \]

2. **Solve for \( y \)**:  
   Divide both sides of the equation by \( -3 \) to isolate \( y \):
   \[
   y = \frac{-3x + 18}{-3}
   \]

3. **Simplify the right-hand side**:  
   Simplify each term:
   \[
   y = x - 6
   \]

Thus, the equation in slope-intercept form is:
\[
y = x - 6
\]

In this form, the slope \( m \) is 1 and the y-intercept \( b \) is -6.

Would you like further clarification, or do you have any questions?

Here are 5 related questions to deepen understanding:
1. What is the slope of the line \( y = x - 6 \)?
2. How would the line \( y = x - 6 \) appear on a graph?
3. How can you verify that \( y = x - 6 \) is equivalent to the original equation \( 3x - 3y = 18 \)?
4. What would happen to the line if the equation were \( 3x - 3y = 12 \) instead?
5. How can the slope-intercept form be used to determine the x-intercept?

**Tip**: When converting an equation to slope-intercept form, always focus on isolating \( y \) and simplify carefully!

Put the following equation of a line into slope-intercept form, simplifying all fractions.
3x − 3y = 18

Learn how to convert the linear equation 3x - 3y = 18 into slope-intercept form (y = mx + b), with step-by-step simplification of fractions. This algebra problem is ideal for students in Grades 7-9.

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