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Rewrite the following equation in slope-intercept form and show your work.

To rewrite the equation in slope-intercept form, let's start with the given equation:

\[
-2x + 3y = 6
\]

The slope-intercept form of a line is:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept. To rewrite the equation in this form, we need to isolate \( y \) on one side of the equation.

### Step 1: Move \( -2x \) to the other side
\[
3y = 2x + 6
\]

### Step 2: Divide each term by 3 to solve for \( y \)
\[
y = \frac{2}{3}x + 2
\]

### Final Answer
The equation in slope-intercept form is:

\[
y = \frac{2}{3}x + 2
\]

In this form:
- The slope \( m \) is \( \frac{2}{3} \).
- The y-intercept \( b \) is 2.

Would you like more details or have any questions?

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### Related Questions
1. What is the interpretation of the slope \( \frac{2}{3} \) in this context?
2. How can you graph this line using the slope and y-intercept?
3. How would this equation change if the right side was set to a different constant?
4. Can this line be parallel or perpendicular to another line? How can we determine that?
5. What is the x-intercept of this line?

### Tip
When rewriting equations, always aim to isolate \( y \) for easier interpretation of slope and y-intercept.

Rewrite the following equation in slope-intercept form and show your work: -2x + 3y = 6

Learn how to rewrite the linear equation -2x + 3y = 6 in slope-intercept form with a step-by-step solution. This problem covers fundamental algebraic concepts, ideal for students in Grades 7-9.

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