To determine the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is -6 using the formula [tex]\( y = |x| + 6 \)[/tex], follow these steps:
1. Start with the given formula:
[tex]\[
y = |x| + 6
\][/tex]
2. Substitute [tex]\( x \)[/tex] with -6:
[tex]\[
y = |-6| + 6
\][/tex]
3. Calculate the absolute value of -6. Recall that the absolute value of a negative number is its positive counterpart:
[tex]\[
|-6| = 6
\][/tex]
4. Now add 6 to the result from the absolute value calculation:
[tex]\[
y = 6 + 6
\][/tex]
5. Perform the addition:
[tex]\[
y = 12
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is -6 is [tex]\( y = 12 \)[/tex].
