Certainly! To determine the [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = 8x + 75 \)[/tex], let's break down the equation step-by-step.
The standard form of a linear equation is:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
The [tex]\( y \)[/tex]-intercept is the point where the line crosses the [tex]\( y \)[/tex]-axis. This occurs when [tex]\( x = 0 \)[/tex]. At this point, the value of [tex]\( y \)[/tex] is simply [tex]\( b \)[/tex] from the equation [tex]\( y = mx + b \)[/tex].
In the equation [tex]\( y = 8x + 75 \)[/tex]:
- [tex]\( m \)[/tex] (the slope) is 8.
- [tex]\( b \)[/tex] (the [tex]\( y \)[/tex]-intercept) is 75.
When [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 8(0) + 75 \][/tex]
[tex]\[ y = 75 \][/tex]
Thus, the [tex]\( y \)[/tex]-intercept is 75. This means the line crosses the [tex]\( y \)[/tex]-axis at the point [tex]\((0, 75)\)[/tex].
So the correct answer is:
A. [tex]\((0, 75)\)[/tex]
