To solve for the x-intercept and y-intercept of the given equation $2x + 4y = -12$, follow these steps:

Step 1: Find the x-intercept

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

$2x + 4(0) = -12$

$2x = -12$

$x = -6$

Thus, the x-intercept is $x = -6$.

Step 2: Find the y-intercept

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

$2(0) + 4y = -12$

$4y = -12$

$y = -3$

Thus, the y-intercept is $y = -3$.

Final Answer:

• x-intercept: $(-6, 0)$
• y-intercept: $(0, -3)$

Let me know if you'd like further clarification or additional help! Here are some questions to deepen your understanding:

1. How do x-intercepts and y-intercepts help in graphing a linear equation?
2. Could we rewrite $2x + 4y = -12$ in slope-intercept form ($y = mx + b$)? What is the slope?
3. What happens if the equation changes to $2x + 4y = 0$?
4. How can we verify the intercepts graphically?
5. What is the significance of intercepts in real-world scenarios?

Tip: Always substitute $x = 0$ or $y = 0$ to find the intercepts quickly.