To determine the value of [tex]\( y \)[/tex] when [tex]\( x = -8 \)[/tex] given the equation:
[tex]\[ y = |x| + 4 \][/tex]
we need to follow these steps:
1. Substitute [tex]\( x \)[/tex] with -8:
Substitute [tex]\( x \)[/tex] in the equation with the given value, [tex]\(-8\)[/tex].
[tex]\[ y = |-8| + 4 \][/tex]
2. Find the absolute value of [tex]\(-8\)[/tex]:
The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore,
[tex]\[ |-8| = 8 \][/tex]
3. Add 4 to the absolute value:
Now that we have the absolute value of [tex]\(-8\)[/tex] which is [tex]\( 8 \)[/tex], we add [tex]\( 4 \)[/tex] to this value:
[tex]\[ y = 8 + 4 \][/tex]
4. Perform the addition:
Summing these up,
[tex]\[ y = 12 \][/tex]
So, the value of [tex]\( y \)[/tex] when [tex]\( x = -8 \)[/tex] is:
[tex]\[ \boxed{12} \][/tex]
