Final Answer:
1. A linear function is a function whose graph is a straight line.
2. Linear functions have a constant rate of change; nonlinear functions do not have a constant rate of change.
3. Linear functions are not constant (unless slope = 0, but generally they can change); nonlinear functions are not constant.
4. Graphs: First graph (straight line) → Linear; second graph (curve) → Nonlinear.
5. Table 1 (x: 2→3→4, y: 5→3→1): constant decrease of 2 → Linear.
Table 2 (x: 16→18→20, y: −20→15→−10): changes are +35, −25 → Not constant → Nonlinear.
6. Table 3: x increases by 1, y increases by 3 each time → Linear.
Table 4: x increases by 1, y changes: +3, +5, +7 → Not constant → Nonlinear.
7. You can tell if a function is linear or nonlinear from a table of values by checking whether the change in y is constant for equal changes in x.
8. Check the tables over equal intervals (e.g., Δx = 1), and see if Δy is the same each time.
9. Equation $3y = 2x + 6$ → rewrite as $y = \frac{2}{3}x + 2$: linear.
Equation $y = 2x^2 + 6$: has $x^2$, so nonlinear.
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Parent Tip: Review the logic above to help your child master the concept of linear and nonlinear functions worksheet.
