Let’s analyze the table to determine if the function is linear or not linear.

Given values:

Steps to check if the function is linear:

A function is linear if there is a constant rate of change between the values of $x$ and $y$. In other words, the slope (rate of change) should remain the same between every pair of points.

Calculate the slope ($m$) between two points:

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Check between each pair of points:

1. Between $(-4, -3)$ and $(0, 0)$: $m = \frac{0 - (-3)}{0 - (-4)} = \frac{3}{4}$

2. Between $(0, 0)$ and $(4, 3)$: $m = \frac{3 - 0}{4 - 0} = \frac{3}{4}$

3. Between $(4, 3)$ and $(8, 6)$: $m = \frac{6 - 3}{8 - 4} = \frac{3}{4}$

Conclusion:

Since the slope remains constant at $\frac{3}{4}$ between all points, the function is linear.

Answer:

✅ Linear

Would you like a detailed explanation on how to graph this function or apply it to real-life examples?

Here are 5 follow-up questions you might want to consider:

1. How do you graph a linear function based on a table?
2. What does the slope $\frac{3}{4}$ represent in this context?
3. How can you identify a linear function just by looking at a table?
4. What are real-life examples of linear functions?
5. How do you convert a table of values into a linear equation?

Tip: A linear function will always produce a straight line when graphed!