To solve this problem, let's first express the interval $[0, 9]$ in set-builder notation.

Set-Builder Notation

The interval $[0, 9]$ includes all real numbers $x$ such that $x$ is greater than or equal to 0 and less than or equal to 9. In set-builder notation, this is written as:

$\{ x \mid 0 \leq x \leq 9 \}$

Graphing on a Number Line

To graph the interval $[0, 9]$ on a number line:

1. Draw a horizontal line representing the number line.
2. Mark the points at 0 and 9 on this line.
3. Draw solid circles (or closed dots) at both 0 and 9 to indicate that these points are included in the interval.
4. Shade the line segment between 0 and 9 to show all the numbers that are included in this interval.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. How would you express the interval $(2, 7]$ in set-builder notation?
2. What is the set-builder notation for the interval $[-4, 0)$?
3. How do you represent the union of two intervals on a number line?
4. What is the difference between open and closed intervals?
5. How do you graph the interval $(-\infty, 3)$ on a number line?

Tip: When converting intervals to set-builder notation, remember to use inequality symbols that match the endpoints of the interval: "<" for open intervals and "≤" for closed intervals.