Gina wrote the following equation on the board 6x + 2y = 12.

Part A: Which of the following points represent the x-intercept and y-intercept of the equation Gina wrote? Select all that apply.
A.(6,0)
B.(0,6)
C.(0,2)
D.(2,0)
E.(0,0)

To find the intercepts of the equation \( 6x + 2y = 12 \), let's determine both the x-intercept and the y-intercept.

### X-intercept:
The x-intercept occurs when \( y = 0 \). Substitute \( y = 0 \) into the equation:
\[
6x + 2(0) = 12 \implies 6x = 12 \implies x = \frac{12}{6} = 2
\]
So, the x-intercept is \( (2, 0) \).

### Y-intercept:
The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation:
\[
6(0) + 2y = 12 \implies 2y = 12 \implies y = \frac{12}{2} = 6
\]
So, the y-intercept is \( (0, 6) \).

### Conclusion:
- The x-intercept is \( (2, 0) \), which corresponds to option D.
- The y-intercept is \( (0, 6) \), which corresponds to option B.

Thus, the correct answers are:
- B. \( (0, 6) \)
- D. \( (2, 0) \)

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Do you want further details on how to graph these intercepts or have any questions?

Here are 5 related questions:
1. How do you find intercepts for equations in standard form?
2. Can an equation have multiple x- or y-intercepts?
3. What happens if the equation has no intercepts?
4. How do you find the slope of the equation \( 6x + 2y = 12 \)?
5. What is the significance of the intercepts in a real-world scenario?

**Tip:** Always remember that the x-intercept is where \( y = 0 \) and the y-intercept is where \( x = 0 \).

Learn how to find the x-intercept and y-intercept of the linear equation 6x + 2y = 12. This algebra problem involves determining where the line crosses the x-axis and y-axis, using simple substitution. Suitable for students in Grades 6-8.

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