High School

A rectangular field is x feet wide and x + 2 feet long. The equation [tex]y = x^2 + 2x[/tex] gives the area of the field in square feet. Determine whether the relationship between x and y is linear and, if so, whether it is proportional.

A) The relationship is linear and proportional.
B) The relationship is linear but not proportional.
C) The relationship is not linear.

Answer :

Final answer:

The relationship between x and y is not linear and not proportional.

Explanation:

The relationship between x and y is not linear.



To determine whether the relationship is proportional, we need to check if the ratio of the areas is constant. The area of the rectangular field is given by the equation y = x^2 + 2x. When we calculate the ratio of the areas of two fields with different widths, the ratio will include terms with x, x+2, and their squares. Since these terms are not linearly related, the relationship is not proportional.

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