To determine the [tex]$y$[/tex]-intercept of the line given by the equation [tex]\( y = 3x - 11 \)[/tex], we need to find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0. This is because, by definition, the [tex]$y$[/tex]-intercept is the point where the line crosses the [tex]$y$[/tex]-axis, and this occurs when [tex]\( x \)[/tex] is 0.
Here’s the step-by-step process:
1. Identify the equation: The line equation given is [tex]\( y = 3x - 11 \)[/tex].
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = 3(0) - 11
\][/tex]
3. Calculate the [tex]$y$[/tex] value:
[tex]\[
y = 0 - 11
\][/tex]
[tex]\[
y = -11
\][/tex]
4. Determine the point: The [tex]$y$[/tex]-intercept occurs when [tex]\( x = 0 \)[/tex], and we have found [tex]\( y = -11 \)[/tex]. Therefore, the [tex]$y$[/tex]-intercept is the point [tex]\((0, -11)\)[/tex].
Given the options:
A. [tex]\((0, -11)\)[/tex]
B. [tex]\((0, -3)\)[/tex]
C. [tex]\((0, 11)\)[/tex]
D. [tex]\((0, 3)\)[/tex]
The correct answer is:
A. [tex]\((0, -11)\)[/tex]
