Based on the image, the task is to identify the correct interval based on the graphical representation on the number line.

The arrow on the number line starts at $-7$ and goes toward $10$, including $10$ (indicated by a closed circle) but not including $-7$ (indicated by an open circle).

Thus, the correct interval is:

$m \in (-\infty, 10]$

This matches the third option in the list.

Would you like further clarification or details? Here are five related questions to deepen your understanding:

1. How do open and closed circles represent inclusion and exclusion in intervals?
2. What does the arrow pointing toward $10$ indicate about the direction of the interval?
3. Why is $-7$ excluded from the interval?
4. Can this representation include infinity as a number, or is it just a conceptual boundary?
5. How would this interval be written in set notation?

Tip: Always double-check whether intervals include or exclude boundaries by carefully observing open and closed circles.