To find the [tex]$y$[/tex]-intercept of the linear equation [tex]\(3x + 2y - 18 = 0\)[/tex], follow these steps:
1. Understand the concept of the [tex]$y$[/tex]-intercept: The [tex]$y$[/tex]-intercept occurs where the line crosses the [tex]$y$[/tex]-axis. At this point, the value of [tex]\(x\)[/tex] is [tex]\(0\)[/tex].
2. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
3(0) + 2y - 18 = 0
\][/tex]
3. Simplify the equation:
[tex]\[
0 + 2y - 18 = 0
\][/tex]
[tex]\[
2y - 18 = 0
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
[tex]\[
2y = 18
\][/tex]
[tex]\[
y = \frac{18}{2}
\][/tex]
[tex]\[
y = 9
\][/tex]
5. Identify the coordinates of the [tex]$y$[/tex]-intercept: Since [tex]\(x = 0\)[/tex] and [tex]\(y = 9\)[/tex], the [tex]$y$[/tex]-intercept is [tex]\((0, 9)\)[/tex].
Thus, the best answer to the question is:
B. [tex]\((0, 9)\)[/tex]
