Linear Function Check E10Ccd

1. **State the problem:** We are given a table of values for $x$ and $y$ and need to determine if the function is linear. If it is linear, we must find the common difference. 2. **Recall the rule for linear functions:** A function is linear if the change in $y$ (called the common difference) is constant when $x$ increases by 1. 3. **Calculate the differences in $y$ values:** - From $x=1$ to $x=2$: $16 - 10 = 6$ - From $x=2$ to $x=3$: $20 - 16 = 4$ - From $x=3$ to $x=4$: $24 - 20 = 4$ 4. **Analyze the differences:** The differences are $6$, $4$, and $4$. Since these are not all equal, the function is not linear. 5. **Conclusion:** There is no common difference, so this table does not represent a linear function.