To find the [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = \frac{1}{2} x - 5 \)[/tex], let us recall the standard form of a linear equation, which is:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] represents the slope of the line, and [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, which occurs when [tex]\( x = 0 \)[/tex].
Using the provided equation [tex]\( y = \frac{1}{2} x - 5 \)[/tex]:
1. Identify the coefficient of [tex]\( x \)[/tex], which is [tex]\( \frac{1}{2} \)[/tex]. This represents the slope [tex]\( m \)[/tex].
2. Identify the constant term, which is [tex]\( -5 \)[/tex]. This represents the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex].
From the given equation [tex]\( y = \frac{1}{2} x - 5 \)[/tex], it is clear that the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is [tex]\( -5 \)[/tex].
Therefore, the [tex]\( y \)[/tex]-intercept of the line [tex]\( y = \frac{1}{2} x - 5 \)[/tex] is:
C. [tex]\(-5\)[/tex]
