Final answer:
Samuel is incorrect as age proportionality is not a consistent or guaranteed relationship in families since the ratio of ages changes over time, unlike height and weight which typically increase together, or block heights where a proportional relationship can be clearly defined.
Step-by-step explanation:
Samuel's statement that his sister’s age is proportional to his brother’s age could be misleading. Age proportionality implies that there is a consistent ratio or relationship between two ages. For instance, if Samuel's brother is 10 years old and his sister is 5 years old, their ages have a 2:1 proportion. However, as they both grow older, the age difference remains constant but the ratio of their ages changes, indicating that while there might be a linear relationship in the number of years they differ in age, the ratio (and thus proportionality) alters over time. Therefore, the answer is B) No, because age proportionality is not a guaranteed relationship in families. Proportionality often refers to quantities that change at the same rate, but with age, even if siblings are a certain number of years apart, that doesn't mean their ages will always hold a specific proportional relationship as they grow. Consider the example regarding height and weight to illustrate a proportional relationship: Height and weight are positively correlated. This means that usually, as height increases, typically weight increases as well (Option D). This scenario showcases a proper use of proportionality when there is evidence of a consistent increase in one variable as another increases. Another example using block heights shows a direct proportionality: The change in height is proportional to the original height. In this case, if the original height of Block B is twice that of Block A, it's accurate to say that the change in the height of Block B is also twice that of Block A, signifying a direct proportional relationship.