To determine the rate of change of a linear function represented by a table of values, we need to calculate the change in $y$ for each unit change in $x$.

Let's look at consecutive points in the table:

1. From $x = -4$ to $x = -2$:

   • $y$ changes from $-1$ to $0$.
   • Change in $y$ ( $\Delta y$ ) = $0 - (-1) = 1$.
   • Change in $x$ ( $\Delta x$ ) = $-2 - (-4) = 2$.
   • Rate of change = $\frac{\Delta y}{\Delta x} = \frac{1}{2}$.

2. From $x = -2$ to $x = 0$:

   • $y$ changes from $0$ to $1$.
   • Change in $y$ = $1 - 0 = 1$.
   • Change in $x$ = $0 - (-2) = 2$.
   • Rate of change = $\frac{1}{2}$.

3. From $x = 0$ to $x = 2$:

   • $y$ changes from $1$ to $2$.
   • Change in $y$ = $2 - 1 = 1$.
   • Change in $x$ = $2 - 0 = 2$.
   • Rate of change = $\frac{1}{2}$.

Since the rate of change is consistent at $\frac{1}{2}$ between each consecutive pair of points, we can conclude that the rate of change for this linear function is $\frac{1}{2}$.

Would you like more details, or do you have any questions?

Here are 5 related questions that expand on this topic:

1. How would the rate of change differ if the function were non-linear?
2. Can you write the equation of the line for this function?
3. What is the significance of the rate of change in a real-world context?
4. How can we identify the slope of a function from its graph?
5. What does a negative rate of change indicate?

Tip: The rate of change, or slope, is a key characteristic in identifying linearity in a function. For linear functions, the rate of change is constant across the domain.