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To find the **x-intercept** and **y-intercept** of the given line equation:

\[
6x + 2y = -6
\]

### Finding the x-intercept:
- At the x-intercept, **y = 0**.
- Substitute \( y = 0 \) into the equation:

\[
6x + 2(0) = -6 \implies 6x = -6
\]

- Solve for \( x \):

\[
x = \frac{-6}{6} = -1
\]

So, the **x-intercept** is \( (-1, 0) \).

### Finding the y-intercept:
- At the y-intercept, **x = 0**.
- Substitute \( x = 0 \) into the equation:

\[
6(0) + 2y = -6 \implies 2y = -6
\]

- Solve for \( y \):

\[
y = \frac{-6}{2} = -3
\]

So, the **y-intercept** is \( (0, -3) \).

### Summary:
- x-intercept: \( (-1, 0) \)
- y-intercept: \( (0, -3) \)

Would you like more details or further clarification?

Here are 5 related questions you can explore:
1. How do you find the intercepts of a more complex equation like \( 3x^2 + 2y = 10 \)?
2. How would the intercepts change if the equation was in slope-intercept form \( y = mx + b \)?
3. What is the geometric interpretation of the x- and y-intercepts on a graph?
4. How do you graph a line using just the intercepts?
5. How can you find intercepts when dealing with inequalities like \( 6x + 2y \geq -6 \)?

**Tip:** When finding intercepts, remember that each intercept occurs when the other variable equals zero!

Find the x-intercept and y-intercept of the line 6x + 2y = -6.

Learn how to find the x-intercept and y-intercept of the linear equation 6x + 2y = -6. This algebraic problem covers key concepts in finding intercepts by substituting variables with zero. Suitable for students in Grades 6-8.

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