To find the [tex]\( x \)[/tex]-intercept of the linear equation [tex]\( 3y + 4x = 8 \)[/tex], we need to determine the point where the graph of the equation crosses the [tex]\( x \)[/tex]-axis. The [tex]\( x \)[/tex]-intercept occurs when [tex]\( y = 0 \)[/tex].
Here are the steps to find the [tex]\( x \)[/tex]-intercept:
1. Set [tex]\( y \)[/tex] to 0 in the equation:
[tex]\[
3y + 4x = 8
\][/tex]
[tex]\[
3(0) + 4x = 8
\][/tex]
2. Simplify the equation:
[tex]\[
4x = 8
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{8}{4}
\][/tex]
[tex]\[
x = 2
\][/tex]
Therefore, the [tex]\( x \)[/tex]-intercept is the point where [tex]\( x = 2 \)[/tex] and [tex]\( y = 0 \)[/tex]. This point is represented as the ordered pair [tex]\((2, 0)\)[/tex].
So, the correct answer is [tex]\((2, 0)\)[/tex].
