To determine if a table represents a linear or nonlinear relationship, we need to check the
rate of change. This means looking at how much $y$ changes for every change in $x$.
Step 1: Check the first table (Left)
* Look at the $x$ column: The values go 2, 4, 6, 8. Each step increases by
2 ($+2$).
* Look at the $y$ column: The values go 50, 35, 20, 5.
* From 50 to 35 is a change of
-15.
* From 35 to 20 is a change of
-15.
* From 20 to 5 is a change of
-15.
*
Conclusion: Since the rate of change is constant (it is always -15), this table is
linear.
Step 2: Check the second table (Right)
* Look at the $x$ column: The values go 1, 4, 7, 10. Each step increases by
3 ($+3$).
* Look at the $y$ column: The values go 1, 16, 49, 100.
* From 1 to 16 is a change of
+15.
* From 16 to 49 is a change of
+33.
* From 49 to 100 is a change of
+51.
*
Conclusion: The rate of change is not constant (15, then 33, then 51). Because the amount $y$ changes keeps getting bigger, this table is
nonlinear.
Final Answer:
The table on the left is
linear because it has a constant rate of change (-15). The table on the right is
nonlinear because the rate of change varies (+15, +33, +51).
Parent Tip: Review the logic above to help your child master the concept of linear or nonlinear worksheet.
