5. Felix is buying a car and plans to sell it after a few years. The equation \( C=15,000- \) \( 975 m \) models the relation between the cost of the car, \( C \), in dollars and the number of years, \( m \), he had the car. a. Find the cost if Felix sells his car in 5 years. \( C=15,000-975 \mathrm{~m} \) b. Find the year when Felix car is worth \( \$ 6225 \). c. Interpret the slope and \( C \)-intercept of the equation.

To solve the problem, we will analyze the equation given: \[ C = 15,000 - 975m \] where \( C \) is the cost of the car in dollars and \( m \) is the number of years Felix has owned the car. ### a. Find the cost if Felix sells his car in 5 years. To find the cost after 5 years, we substitute \( m = 5 \) into the equation: \[ C = 15,000 - 975(5) \] Calculating the value: \[ C = 15,000 - 4,875 \] \[ C = 10,125 \] So, the cost of the car after 5 years is **$10,125**. ### b. Find the year when Felix's car is worth $6,225. To find the year when the car is worth $6,225, we set \( C = 6,225 \) and solve for \( m \): \[ 6,225 = 15,000 - 975m \] Rearranging the equation: \[ 975m = 15,000 - 6,225 \] \[ 975m = 8,775 \] Now, divide both sides by 975: \[ m = \frac{8,775}{975} \] \[ m = 9 \] So, Felix's car will be worth **$6,225** after **9 years**. ### c. Interpret the slope and \( C \)-intercept of the equation. 1. **Slope**: The slope of the equation is \(-975\). This means that for each additional year \( m \) that Felix owns the car, the value of the car decreases by $975. This indicates the rate of depreciation of the car's value over time. 2. **\( C \)-intercept**: The \( C \)-intercept is \( 15,000 \). This represents the initial cost of the car when \( m = 0 \) (i.e., when Felix first buys the car). It indicates that the car's value starts at $15,000. In summary: - The slope indicates the annual depreciation of the car's value. - The \( C \)-intercept indicates the initial purchase price of the car.