To rewrite the equation $2x - 3y = 18$ into slope-intercept form ($y = mx + b$), follow these steps:

Step 1: Isolate $y$

The goal is to solve for $y$ in terms of $x$.

1. Start with the equation: $2x - 3y = 18$

2. Subtract $2x$ from both sides: $-3y = -2x + 18$

3. Divide every term by $-3$ to isolate $y$: $y = \frac{-2}{-3}x + \frac{18}{-3}$

Step 2: Simplify

Simplify the fractions: $y = \frac{2}{3}x - 6$

Final Answer:

The equation in slope-intercept form is: $y = \frac{2}{3}x - 6$

If you have any questions or need more help, let me know!

Here are five follow-up questions:

1. How do you determine the slope from the slope-intercept form of a line?
2. What is the y-intercept of the line $y = \frac{2}{3}x - 6$?
3. How can you graph a line using the slope and y-intercept?
4. How does the slope-intercept form differ from the standard form of a line?
5. Why is it important to simplify fractions in the slope-intercept form?

Tip: Always check your work by substituting a point into the final equation to ensure it satisfies the original equation!