Let's determine the [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = -6x - 3 \)[/tex].
The [tex]\( y \)[/tex]-intercept of a line is the point at which it crosses the [tex]\( y \)[/tex]-axis. This point occurs where [tex]\( x = 0 \)[/tex]. To find the [tex]\( y \)[/tex]-intercept, we will substitute [tex]\( x = 0 \)[/tex] into the equation and solve for [tex]\( y \)[/tex].
Given the equation:
[tex]\[ y = -6x - 3 \][/tex]
Step 1: Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -6(0) - 3 \][/tex]
Step 2: Simplify the expression:
[tex]\[ y = -3 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the line is [tex]\(-3\)[/tex].
So, the correct answer is:
A. [tex]\(-3\)[/tex]
