To find the [tex]$x$[/tex]-intercept of the line given by the equation [tex]\(3x - y = 6\)[/tex], we need to determine the point where the line crosses the x-axis. The [tex]$x$[/tex]-intercept is the point on the x-axis where the line meets it, and at this point, the [tex]\(y\)[/tex]-coordinate is always zero.
Here are the step-by-step details:
1. Set [tex]\(y = 0\)[/tex] since we know that at the x-intercept, [tex]\(y\)[/tex] must be zero.
2. Substitute [tex]\(y = 0\)[/tex] into the equation [tex]\(3x - y = 6\)[/tex]:
[tex]\[
3x - 0 = 6
\][/tex]
This simplifies to:
[tex]\[
3x = 6
\][/tex]
3. To solve for [tex]\(x\)[/tex], divide both sides of the equation by 3:
[tex]\[
x = \frac{6}{3} = 2
\][/tex]
Hence, the [tex]$x$[/tex]-coordinate of the intercept is 2.
Therefore, the coordinates of the [tex]$x$[/tex]-intercept are [tex]\((2, 0)\)[/tex].
So, the correct choice is:
[tex]\[
(2, 0)
\][/tex]
