To identify the rate of change for a linear function from a table, we need to calculate the slope, which is given by the formula:

$\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Let's compute this from the table:

For the points $(x_1, y_1) = (0, -3)$ and $(x_2, y_2) = (4, -10)$, we can plug the values into the slope formula:

$\text{slope} = \frac{-10 - (-3)}{4 - 0} = \frac{-10 + 3}{4} = \frac{-7}{4}$

Thus, the rate of change (slope) is $-\frac{7}{4}$.

Would you like further explanation or more details?

Here are 5 follow-up questions for deeper understanding:

1. How would you interpret the rate of change in a real-world context?
2. What is the significance of a negative slope in a linear function?
3. How can you use the slope to find the equation of the line?
4. What other pairs of points from the table could you use to verify the slope?
5. How would the graph of this function look based on the rate of change?

Tip: The slope tells you how steep a line is and whether it increases or decreases as you move from left to right on the graph.