To determine where the line [tex]\( y = 3x + 5 \)[/tex] crosses the [tex]\( y \)[/tex]-axis, we need to find the point on the line where [tex]\( x = 0 \)[/tex]. This is because the [tex]\( y \)[/tex]-axis is where [tex]\( x \)[/tex] is equal to zero.
1. Start with the equation of the line:
[tex]\[
y = 3x + 5
\][/tex]
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = 3(0) + 5
\][/tex]
3. Simplify the equation:
[tex]\[
y = 5
\][/tex]
Thus, the line [tex]\( y = 3x + 5 \)[/tex] crosses the [tex]\( y \)[/tex]-axis at [tex]\( y = 5 \)[/tex].
Therefore, the correct answer is:
```
at [tex]$y=5$[/tex]
```
