The chart shows the measurements of the height of a child at 3, 6, and 9 months of age. The equation H = T + 21 models the relationship between the height H, in inches, and age T, in months. Which of the following statements is true about the dependent variable in the relationship?
Height is the dependent variable because the height of the child depends on the length of time that has passed since birth.
In this relationship, height (H) is determined by age (T), making height the dependent variable that relies on the age of the child, which progresses over time since birth.
This statement is incorrect because the height of the child does not directly depend on the length of the mother's pregnancy. Instead, height is influenced by the time elapsed after birth, reflecting the child's growth over months rather than prenatal factors.
This choice misrepresents the relationship by suggesting that time is dependent. In fact, age (time) is the independent variable that progresses linearly, while height is what changes in relation to that time.
This statement is misleading as it implies that time relies on the measurements taken. Rather, the measurements are taken at set intervals (every 3 months), but it is the height that changes in response to the independent variable of age.
In this context, height is clearly the dependent variable as it is contingent upon the independent variable, which is the age of the child. The relationship modeled by the equation H = T + 21 illustrates how height increases with the passage of time since birth, confirming that age is the factor determining height, not the other way around.
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