To solve this problem, we will compare the provided number line graph with each mathematical expression.

The number line shows a movement starting at $-7$, moving right to $6$ (represented by the arrow ending at $6$) and then moving left back to $-3$.

Now, let's break down each of the options:

Option a) $-7 + 13 - 9$

1. Start at $-7$.
2. Add $13$: $-7 + 13 = 6$ So you move from $-7$ to $6$.
3. Subtract $9$: $6 - 9 = -3$ So you move back from $6$ to $-3$.

This matches the graph perfectly, which shows a movement from $-7$ to $6$, then back to $-3$.

Option b) $-7 - 13 + 9$

1. Start at $-7$.
2. Subtract $13$: $-7 - 13 = -20$ This does not match the graph.

Option c) $-7 - 13 - 9$

1. Start at $-7$.
2. Subtract $13$: $-7 - 13 = -20$ Again, this does not match the graph.

Conclusion:

The correct option is a) $-7 + 13 - 9$, as it matches the movements shown on the number line.

Would you like further explanation or have any questions?

Related Questions:

1. How do you interpret positive and negative movements on a number line?
2. What are the steps to solving arithmetic problems with multiple operations?
3. Can you explain how to visualize adding and subtracting integers on a number line?
4. How does order of operations affect these kinds of expressions?
5. What other ways can we represent movements on a number line?

Tip: When working with a number line, always break down each step (addition or subtraction) and follow the direction (left or right) based on the sign of the number.