To find the y-intercept of the line represented by the equation [tex]\( y = -3x - 8 \)[/tex], we need to identify the point where the line crosses the y-axis.
When a line crosses the y-axis, the value of [tex]\( x \)[/tex] is 0. Therefore, we substitute [tex]\( x \)[/tex] with 0 in the given equation.
Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = -3x - 8 \)[/tex]:
[tex]\[ y = -3(0) - 8 \][/tex]
This simplifies to:
[tex]\[ y = -8 \][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( y = -8 \)[/tex]. This means the y-intercept of the line is the point [tex]\( (0, -8) \)[/tex].
Therefore, the correct answer is:
C) [tex]\( (0, -8) \)[/tex]
