To determine the interval where the function is both increasing and linear, we need to carefully analyze the graph.

From the graph:

1. A linear function has a constant slope, meaning it appears as a straight line.
2. An increasing function has a positive slope (the graph rises as you move from left to right).

Let's examine the intervals:

• Between $x = -9$ and $x = -4$: The function is decreasing (the graph slopes downward), so this is not the correct interval.
• Between $x = -4$ and $x = -1$: The graph is non-linear, curving up and down. So, this is also incorrect.
• Between $x = -1$ and $x = 5$: The function is increasing from $x = -1$ to $x = 1$, but only a portion is linear.
• Between $x = 5$ and $x = 9$: The function is increasing, but the graph is not linear here. The curve shows a slope change, indicating it's non-linear.

The correct interval is between $x = -1$ and $x = 5$, as this contains a portion that is increasing and linear (a straight, rising line).

Would you like more details on this? Here are 5 related questions you might explore:

1. What distinguishes a linear from a non-linear function in general?
2. How can we identify increasing vs decreasing intervals on a graph?
3. Can a function be increasing but non-linear?
4. How does one calculate the slope of a linear function from a graph?
5. What does it mean if a function is decreasing and linear?

Tip: Always check both the slope and the shape of the graph to determine if a function is increasing/decreasing and linear/non-linear!