The inequality given is $|y| \leq 8$, which means we need to find all values of $y$ such that the absolute value of $y$ is less than or equal to 8.

To solve this:

1. We rewrite the absolute value inequality $|y| \leq 8$ as a compound inequality: $-8 \leq y \leq 8$ This means $y$ can be any number between -8 and 8, inclusive.

2. To graph this on a number line:

   • Place solid dots at $-8$ and $8$ because the inequality includes the endpoints (indicated by $\leq$).
   • Shade the region between $-8$ and $8$, including all the numbers in this range.

This is how the graph would look:

• The number line extends from $-10$ to $10$.
• Solid dots at $-8$ and $8$.
• A shaded line between $-8$ and $8$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you solve absolute value inequalities with $\geq$ instead of $\leq$?
2. How can you solve an absolute value inequality like $|y + 3| \leq 5$?
3. What happens if the inequality is $|y| > 8$ instead of $\leq 8$?
4. Can absolute value inequalities have no solution?
5. How does the solution change if the absolute value inequality includes a negative number?

Tip: For absolute value inequalities, if you have $|x| \leq a$, always remember this means $-a \leq x \leq a$.