To find the $x$-intercept and $y$-intercept of the equation $2x + 3y = 12$, we follow these steps:

1. Find the $x$-intercept:

The $x$-intercept occurs when $y = 0$. Substituting $y = 0$ into the equation: $2x + 3(0) = 12 \implies 2x = 12 \implies x = 6.$ Thus, the $x$-intercept is at $(6, 0)$.

2. Find the $y$-intercept:

The $y$-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation: $2(0) + 3y = 12 \implies 3y = 12 \implies y = 4.$ Thus, the $y$-intercept is at $(0, 4)$.

Summary:

• $x$-intercept: $(6, 0)$
• $y$-intercept: $(0, 4)$

Would you like a graph of this or further clarification?

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Related Questions:

1. How can you rewrite the equation in slope-intercept form?
2. What are the coordinates of points where $x = 3$ and $y = 2$?
3. How do you find the slope of the line $2x + 3y = 12$?
4. Can this equation represent a real-world situation? If so, give an example.
5. What is the general form of a linear equation, and how does this equation fit it?

Tip: Always check by substituting the intercept values back into the equation to verify correctness!