What is the rate of change of the balance with respect to the number of deposits?
Understand the Problem
The question is asking to determine the rate of change of Tobias' savings account balance in relation to the number of deposits, as represented by the linear graph provided.
Answer
The rate of change is $50 \text{ dollars per deposit}$.
Answer for screen readers
The rate of change of the balance with respect to the number of deposits is $50 \text{ dollars per deposit}$.
Steps to Solve
- Identify Points on the Graph
Choose two points on the line graph. For example, $(2, 150)$ and $(5, 300)$.
- Calculate the Change in Balance
Subtract the y-coordinates (balance values) of the two points: $$ \text{Change in Balance} = 300 - 150 = 150 \text{ dollars} $$
- Calculate the Change in Deposits
Subtract the x-coordinates (number of deposits) of the two points: $$ \text{Change in Deposits} = 5 - 2 = 3 \text{ deposits} $$
- Determine the Rate of Change
The rate of change is found by dividing the change in balance by the change in deposits: $$ \text{Rate of Change} = \frac{\text{Change in Balance}}{\text{Change in Deposits}} = \frac{150}{3} = 50 \text{ dollars/deposit} $$
The rate of change of the balance with respect to the number of deposits is $50 \text{ dollars per deposit}$.
More Information
In a linear relationship, the rate of change shows how much one quantity changes in relation to another. In this case, it indicates that each deposit increases the balance by $50.
Tips
- Forgetting to use the correct points from the graph to determine the changes can lead to an incorrect calculation of the rate of change.
- Using slope incorrectly; remember that the slope is calculated by change in y over change in x.
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