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The average weight in pounds of American men in their sixties (in 1979) as a function of their heights in inches is given:

Height (h): 68 69 70 71 72 73
Weight (w): 166 171 176 181 186 191

(a) How do you know from the table that weight \( w \) is a linear function of height \( h \)?

Answer :

Final answer:

Weight w can be considered a linear function of height h if there's a constant rate of change. The given data shows a constant increase of 5 pounds in weight for each one-inch increase in height, confirming the linear relationship.

Explanation:

To determine whether weight w is a linear function of height h, we should look for a constant rate of change in weight as height increases.

From the given table, we can calculate the differences in weight for each one-inch increase in height. If these differences are constant, we can conclude that there is a linear relationship between weight and height.

Let's calculate the rate of change in weight for each one-inch increment in height:

  • For height increasing from 68 to 69 inches, weight increases from 166 to 171 pounds, a change of 5 pounds.
  • For height increasing from 69 to 70 inches, weight increases from 171 to 176 pounds, also a change of 5 pounds.
  • This pattern continues, with the weight increasing by 5 pounds for each increase of one inch in height.

Since the rate of change (5 pounds per inch) is constant, we can conclude that weight is a linear function of height for American men in their sixties (in 1979) based on the data provided.

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Rewritten by : Barada