To find the [tex]$y$[/tex]-intercept of the equation [tex]\( y = -10 + 3x \)[/tex], we need to determine the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
Step-by-step:
1. Start with the given equation:
[tex]\[
y = -10 + 3x
\][/tex]
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = -10 + 3(0)
\][/tex]
3. Simplify the equation:
[tex]\[
y = -10 + 0
\][/tex]
4. This simplifies further to:
[tex]\[
y = -10
\][/tex]
Hence, the [tex]$y$[/tex]-intercept, where [tex]\( x = 0 \)[/tex], is:
[tex]\[
(0, -10)
\][/tex]
Among the given options:
- [tex]\((0, -10)\)[/tex]
- [tex]\((0, 10/3)\)[/tex]
- [tex]\((0, 10)\)[/tex]
- [tex]\((0, -10/3)\)[/tex]
The correct option is:
[tex]\[
\boxed{(0, -10)}
\][/tex]
