To find the coordinates of the [tex]\( x \)[/tex]-intercept of the line represented by the equation [tex]\( 2x - y = 6 \)[/tex], we need to determine the point where the line crosses the [tex]\( x \)[/tex]-axis. At the [tex]\( x \)[/tex]-intercept, the value of [tex]\( y \)[/tex] is [tex]\( 0 \)[/tex].
Here is a detailed, step-by-step solution:
1. Set [tex]\( y = 0 \)[/tex] in the equation [tex]\( 2x - y = 6 \)[/tex]:
[tex]\[
2x - 0 = 6
\][/tex]
2. Simplify the equation:
[tex]\[
2x = 6
\][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{6}{2} = 3
\][/tex]
Therefore, the [tex]\( x \)[/tex]-intercept occurs at the point where [tex]\( x = 3 \)[/tex] and [tex]\( y = 0 \)[/tex]. The coordinates of the [tex]\( x \)[/tex]-intercept are:
[tex]\[
(3, 0)
\][/tex]
Thus, the correct answer is:
[tex]\[
(3, 0)
\][/tex]
