To find the [tex]$y$[/tex]-intercept of the line defined by the equation [tex]\(y = -6x - 3\)[/tex], we need to determine the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex].
The [tex]$y$[/tex]-intercept is the point where the line crosses the [tex]$y$[/tex]-axis. At this point, the value of [tex]\(x\)[/tex] is always zero.
1. Substitute [tex]\(x = 0\)[/tex] into the equation [tex]\(y = -6x - 3\)[/tex]:
[tex]\[
y = -6(0) - 3
\][/tex]
2. Simplify the equation:
[tex]\[
y = -3
\][/tex]
Therefore, the [tex]$y$[/tex]-intercept of the line [tex]\(y = -6x - 3\)[/tex] is [tex]\(-3\)[/tex].
The correct answer is:
D. [tex]\(-3\)[/tex]
