To determine the [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = -3x + 7 \)[/tex], we need to find the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]. The [tex]\( y \)[/tex]-intercept is simply the point where the line crosses the [tex]\( y \)[/tex]-axis.
Given the equation:
[tex]\[ y = -3x + 7 \][/tex]
Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -3(0) + 7 \][/tex]
This simplifies to:
[tex]\[ y = 0 + 7 \][/tex]
[tex]\[ y = 7 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the line is 7.
So, the correct answer is:
B. 7
