Questions: Question 15 Catherine just graduated and wants to spend time off in Atlanta. Before graduating, she saved 7000 for this trip and plans to spend 600 per week for food, rent and activities. If she graphs her amount, A, of savings in dollars and the time, t, in weeks since the trip started, a) which variable would be the dependent variable and which would be independent? The time t is the dependent variable and the amount A is the independent variable. The amount A is the dependent variable and the time t is the independent variable. b) on which axes would the variables be most commonly shown? The amount, A, would commonly be the vertical (y) axis and the time, t, would be the horizontal (x) axis. The time, t, would commonly be the vertical (y) axis and the amount, A, would be the horizontal (x) axis. c) give the coordinates of the vertical intercept d) give the coordinates of the horizontal intercept e) which is the best interpretation of the vertical intercept represent? f) which is the best interpretation the horizontal intercept represent?

Solution Steps

a) The dependent variable is the one that depends on the other variable. In this case, the amount of savings \( A \) depends on the time \( t \), so \( A \) is the dependent variable and \( t \) is the independent variable.

b) In a graph, the independent variable is typically shown on the horizontal axis (x-axis), and the dependent variable is shown on the vertical axis (y-axis). Therefore, the amount \( A \) would be on the y-axis, and the time \( t \) would be on the x-axis.

c) The vertical intercept occurs when the time \( t = 0 \). At this point, the amount \( A \) is equal to the initial savings, which is $7000.

In the given problem, Catherine's savings amount \( A \) and the time \( t \) in weeks are the two variables. We need to determine which is the dependent variable and which is the independent variable.

• The amount of savings \( A \) depends on the time \( t \) because as time progresses, Catherine spends money, reducing her savings. Therefore, \( A \) is the dependent variable, and \( t \) is the independent variable.

In a typical graph:

• The independent variable is plotted on the horizontal axis (x-axis).
• The dependent variable is plotted on the vertical axis (y-axis).

Thus, the amount \( A \) would commonly be the vertical (y) axis, and the time \( t \) would be the horizontal (x) axis.

The vertical intercept occurs when \( t = 0 \). At the start of the trip, Catherine has her full savings amount:

\[ A = 7000 \]

Thus, the coordinates of the vertical intercept are \((0, 7000)\).

Final Answer