To find the x-intercept and y-intercept for the given equation $2x + 3y = 6$:

1. X-intercept

The x-intercept occurs when $y = 0$. Substitute $y = 0$ into the equation:

$2x + 3(0) = 6$

$2x = 6 \implies x = 3$

So, the x-intercept is $3$, which is already provided.

2. Y-intercept

The y-intercept occurs when $x = 0$. Substitute $x = 0$ into the equation:

$2(0) + 3y = 6$

$3y = 6 \implies y = 2$

So, the y-intercept is $2$.

Final Answer:

• X-intercept: $3$
• Y-intercept: $2$

Let me know if you'd like further clarification on the steps! Here are some related questions to practice:

1. What are the intercepts of $4x + 5y = 20$?
2. How do you graph a line given its intercepts?
3. Can you derive the slope from the intercepts?
4. What happens to the intercepts if you multiply the equation by a constant?
5. How do intercepts relate to the slope-intercept form of an equation?

Tip: When finding intercepts, always substitute $y = 0$ for the x-intercept and $x = 0$ for the y-intercept.