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?

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.