Certainly! Let's analyze the problem step-by-step:
1. Initial Value: The car is purchased at a value of [tex]$10,000. This means that at the starting point (i.e., at \( x = 0 \) years), the value of the car \( y \) is $[/tex]10,000.
2. Depreciation Rate: The car depreciates by [tex]$750 every year. This implies that the value of the car decreases by $[/tex]750 for each year [tex]\( x \)[/tex].
3. Formulating the Equation:
- We need to express the value of the car [tex]\( y \)[/tex] after [tex]\( x \)[/tex] years.
- Initially, the value is [tex]$10,000.
- For each year \( x \), we subtract $[/tex]750 from the initial value.
4. Mathematical Representation:
- The initial value is subtracted by [tex]\( 750 \times x \)[/tex] (since $750 depreciation multiplied by the number of years [tex]\( x \)[/tex]).
5. Putting It All Together:
- The equation that models the car's depreciation can be written as:
[tex]\[
y = 10000 - 750 x
\][/tex]
6. Choosing the Correct Option:
- Among the given options, the equation that matches our derived formula is:
[tex]\[
\boxed{y = 10000 - 750 x}
\][/tex]
Thus, the best equation that models the depreciation of the car is:
A. [tex]\( y = 10000 - 750 x \)[/tex]
