Sure! Let's find the [tex]\( x \)[/tex]-intercept of the equation [tex]\( y = -2x + 6 \)[/tex].
The [tex]\( x \)[/tex]-intercept is the point where the graph intersects the [tex]\( x \)[/tex]-axis. At the [tex]\( x \)[/tex]-intercept, the value of [tex]\( y \)[/tex] is 0. So we set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
1. Start with the given equation:
[tex]\[
y = -2x + 6
\][/tex]
2. Set [tex]\( y = 0 \)[/tex] because at the [tex]\( x \)[/tex]-intercept, [tex]\( y \)[/tex] is zero:
[tex]\[
0 = -2x + 6
\][/tex]
3. Solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]:
[tex]\[
-2x + 6 = 0
\][/tex]
[tex]\[
-2x = -6
\][/tex]
[tex]\[
x = 3
\][/tex]
So, the [tex]\( x \)[/tex]-intercept is at the point [tex]\((3, 0)\)[/tex]. Therefore, the correct answer is:
[tex]\((3, 0)\)[/tex]
