To find the intercepts of the equation [tex]\(2x + 6y = 12\)[/tex], we need to determine the points where the line crosses the x-axis and the y-axis.
1. Finding the x-intercept:
- The x-intercept occurs where the line crosses the x-axis, which means [tex]\(y = 0\)[/tex].
- Substitute [tex]\(y = 0\)[/tex] into the equation [tex]\(2x + 6y = 12\)[/tex].
[tex]\[
2x + 6(0) = 12
\][/tex]
This simplifies to:
[tex]\[
2x = 12
\][/tex]
Solving for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{12}{2} = 6
\][/tex]
- Therefore, the x-intercept is [tex]\((6, 0)\)[/tex].
2. Finding the y-intercept:
- The y-intercept occurs where the line crosses the y-axis, which means [tex]\(x = 0\)[/tex].
- Substitute [tex]\(x = 0\)[/tex] into the equation [tex]\(2x + 6y = 12\)[/tex].
[tex]\[
2(0) + 6y = 12
\][/tex]
This simplifies to:
[tex]\[
6y = 12
\][/tex]
Solving for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{12}{6} = 2
\][/tex]
- Therefore, the y-intercept is [tex]\((0, 2)\)[/tex].
Given these calculations, the intercepts of the equation [tex]\(2x + 6y = 12\)[/tex] are [tex]\((6, 0)\)[/tex] and [tex]\((0, 2)\)[/tex].
Thus, the correct answer is:
[tex]\[
(6, 0) \text{ and } (0, 2)
\][/tex]
