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At the beginning of the year, Adrian's savings account balance was $28. Each week, he deposits another $15 into that account, and he doesn't spend any of his savings. Is his savings account balance proportional to the number of weeks since the start of the year? Choose 1 answer: (A) Yes (B) No

At the beginning of the year, Adrian's savings account balance was $28 \$ 28 . Each week, he deposits another $15 \$ 15 into that account, and he doesn't spend any of his savings.\newlineIs his savings account balance proportional to the number of weeks since the start of the year?\newlineChoose 11 answer:\newline(A) Yes\newline(B) No

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Q. At the beginning of the year, Adrian's savings account balance was $28 \$ 28 . Each week, he deposits another $15 \$ 15 into that account, and he doesn't spend any of his savings.\newlineIs his savings account balance proportional to the number of weeks since the start of the year?\newlineChoose 11 answer:\newline(A) Yes\newline(B) No
  1. Define Variables: Let's define the variables:\newlineLet SS be the savings account balance.\newlineLet ww be the number of weeks since the start of the year.\newlineThe initial balance is $28\$28, and Adrian deposits $15\$15 each week.\newlineThe relationship between the savings account balance and the number of weeks can be described by the equation S=28+15wS = 28 + 15w.
  2. Check Proportionality: To determine if the savings account balance is proportional to the number of weeks, we need to check if the relationship between SS and ww is a direct proportion. A direct proportion means that as ww increases, SS increases at a constant rate.\newlineThe equation S=28+15wS = 28 + 15w shows that for every additional week, the savings increase by \(\(15\)), which is a constant rate.
  3. Direct Proportion Criteria: However, for a relationship to be proportional, the ratio of SS to ww must be constant, and the graph of the relationship must pass through the origin (0,0)(0,0). Since there is an initial balance of $28\$28 (when w=0w = 0), the graph of this relationship would not pass through the origin.
  4. Conclusion: Therefore, the savings account balance is not proportional to the number of weeks since the start of the year because of the initial balance that does not fit the criteria for direct proportionality.

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