Here is the graph of the equation \(2x + 3y = 6\). The line crosses the y-axis at \(y = 2\) and the x-axis at \(x = 3\), consistent with the slope-intercept form we derived earlier.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do you determine the slope and intercept from a standard form equation like \(Ax + By = C\)?
2. What is the meaning of the slope \(-\frac{2}{3}\) in the context of this graph?
3. How would the graph change if the equation were \(2x + 3y = 9\) instead?
4. Can you find the distance between the x- and y-intercepts?
5. How would you graph an equation with a vertical or horizontal line?

**Tip:** The slope represents the steepness of the line and can be interpreted as "rise over run." A negative slope means the line is decreasing.

Learn how to graph the linear equation 2x + 3y = 6 by identifying the x- and y-intercepts. This problem covers key concepts in algebra, including converting a standard form equation to slope-intercept form and understanding the meaning of the slope. Suitable for students in Grades 7-9.

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