33. 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?
Answer: B
Height is the dependent variable because the height of the child depends on the length of time that has passed since birth.
In the relationship defined by the equation H = T + 21, height (H) is determined based on the age (T) of the child. This indicates that height is dependent on time, specifically the amount of time that has elapsed since birth.
A) Height is the dependent variable because the height of the child depends on the length of the mother's pregnancy
This statement is incorrect because it misrepresents the relationship modeled by the equation. The height of the child does not depend on the length of the mother's pregnancy; instead, it depends on the child's age after birth.
B) Height is the dependent variable because the height of the child depends on the length of time that has passed since birth
This statement is accurate. The equation indicates that height (H) changes based on age (T), which is measured in months since birth. Therefore, height is indeed the dependent variable, as it relies on the passage of time.
C) Time is the dependent variable because time depends on the number of months that have passed since birth
This statement is incorrect. Time (T) is the independent variable in this context, as it is what influences the dependent variable (height). Time does not depend on height; rather, height changes according to time.
D) Time is the dependent variable because the height measurements of the child are taken every 3 months
This statement is also incorrect. While height measurements are taken at intervals, time itself is not dependent on these measurements; it is the predictor variable that influences changes in height.
Conclusion
The correct answer is B, as it accurately identifies height as the dependent variable that relies on the child's age since birth. The other options either misinterpret the relationship or incorrectly label time as a dependent variable, which does not align with the equation provided. Thus, B is the only option that correctly reflects the nature of the relationship between height and age.