To determine the [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = 5x - 21 \)[/tex], we need to find the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
The [tex]\( y \)[/tex]-intercept is the point where the line crosses the [tex]\( y \)[/tex]-axis. By definition, this occurs when [tex]\( x = 0 \)[/tex].
Let's substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = 5x - 21 \][/tex]
Substituting [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 5(0) - 21 \][/tex]
[tex]\[ y = -21 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept is the point [tex]\((0, -21)\)[/tex].
The correct answer is:
A. [tex]\((0, -21)\)[/tex]
