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Consider a square shaped lunch box whose side length is x inches. The equation which can be formed to represent the area of the box in square inches is y = x2. Make use of the relationship to determine whether the function is linear and state whether it is proportional.
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The area function is y = x².
- Is it linear? No. A linear function has the form y = mx + b (constant rate of change). y = x² is a parabola with a non‑constant rate of change, so it is not linear.
- Is it proportional? No. Proportional means y = kx for some constant k. Although y(0)=0, the ratio y/x = x is not constant (e.g. y/x = 1 when x=1 but =2 when x=2), so y = x² is not proportional.
- Is it linear? No. A linear function has the form y = mx + b (constant rate of change). y = x² is a parabola with a non‑constant rate of change, so it is not linear.
- Is it proportional? No. Proportional means y = kx for some constant k. Although y(0)=0, the ratio y/x = x is not constant (e.g. y/x = 1 when x=1 but =2 when x=2), so y = x² is not proportional.
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