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 $x = 0$.