To find the point of intersection of the line [tex]\(2x + 3y = 6\)[/tex] with the [tex]\(x\)[/tex]-axis, we need to determine the [tex]\(x\)[/tex]-coordinate where this line intersects the [tex]\(x\)[/tex]-axis. On the [tex]\(x\)[/tex]-axis, the [tex]\(y\)[/tex]-coordinate is always 0.
Let's substitute [tex]\(y = 0\)[/tex] into the given equation [tex]\(2x + 3y = 6\)[/tex] and solve for [tex]\(x\)[/tex]:
1. Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[
2x + 3(0) = 6
\][/tex]
2. Simplify the equation:
[tex]\[
2x = 6
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{6}{2} = 3
\][/tex]
So the point of intersection with the [tex]\(x\)[/tex]-axis is [tex]\((3, 0)\)[/tex].
Thus, the correct answer is:
(C) [tex]\((3, 0)\)[/tex]
