The equation given is \( 9y - 3x = 18 \). To solve this equation for \( y \), we'll rearrange it to the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step-by-Step Solution:

1. **Isolate the term with \( y \)**:
   \[
   9y = 3x + 18
   \]

2. **Divide the entire equation by 9** to solve for \( y \):
   \[
   y = \frac{3x}{9} + \frac{18}{9}
   \]
   \[
   y = \frac{1}{3}x + 2
   \]

### Final Answer:
The equation in slope-intercept form is \( y = \frac{1}{3}x + 2 \).

The slope \( m \) is \( \frac{1}{3} \), and the y-intercept \( b \) is 2.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How would you find the x-intercept of the equation \( 9y - 3x = 18 \)?
2. What is the graph of the equation \( y = \frac{1}{3}x + 2 \) like?
3. How does changing the coefficient of \( x \) affect the slope of the line?
4. Can you find the slope of a line perpendicular to \( y = \frac{1}{3}x + 2 \)?
5. What would the equation be if the line were parallel to \( y = \frac{1}{3}x + 2 \) but passed through the point (3, 5)?

**Tip:** When converting an equation to slope-intercept form, remember that the slope indicates how steep the line is, and the y-intercept shows where the line crosses the y-axis.

Learn how to solve the linear equation 9y − 3x = 18 and convert it to slope-intercept form. This problem covers key algebraic concepts like isolating variables and dividing to simplify. Suitable for students in Grades 8-10.

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