To find the slope-intercept form of the equation $2x + 3y = 6$, we need to solve for $y$ in terms of $x$ and write the equation in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Here’s the step-by-step process:

1. Start with the equation: $2x + 3y = 6$

2. Subtract $2x$ from both sides to isolate the $y$ term: $3y = -2x + 6$

3. Divide both sides by 3 to solve for $y$: $y = -\frac{2}{3}x + 2$

Now the equation is in slope-intercept form $y = mx + b$, where:

• The slope ($m$) is $-\frac{2}{3}$.
• The y-intercept ($b$) is $2$.

Do you want more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you find the slope given two points on a line?
2. What is the significance of the y-intercept in a linear equation?
3. How would you convert a slope-intercept form equation back to standard form?
4. Can you graph the equation $y = -\frac{2}{3}x + 2$?
5. What is the effect on the graph if the slope is positive instead of negative?

Tip: When graphing a line, start by plotting the y-intercept and then use the slope to find another point on the line.