Answer:
Option 1
Explanation:
You want to know which of 4 tables shows a non-linear function.
Linear function
A function represented by a data table will be linear if the ratios of changes in y to changes in x are the same for all intervals.
Option 1
Changes in y are ...
-10 -(-4) = -6, -8, -10
Changes in x are ...
10 -8 = 2, 2, 2
The ratios of these changes are ...
-6/2 = -3, -8/2 = -4, =10/2 = -5
These are not constant, so this table is a nonlinear function.
Option 2
Changes in y are ...
8 -10 = -2, -8, -6
Changes in x are ...
-2 -(-3) = 1, 4, 3
The ratios of these changes are ...
-2/1 = -2, -8/4 = -2, -6/3 = -2
These are constant, so this table is a linear function.
The nonlinear function is Option 1.
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Additional comment
The ∆y/∆x ratios for Option 3 are all -10/3. For Option 4, they are all 2.