An SUV is purchased new for $\$ 31,500$. Part: 0 / 4 Part 1 of 4 (a) Write a linear function of the form $y=m t+b$ to represent the value $y$ of the vehicle $t$ years after purchase. Assume that the vehicle is depreciated by $\$ 3150$ per year. The model for the value of the car $t$ years after purchase is $y=$

Step 1 ：An SUV is purchased new for $31,500.

Step 2 ：The vehicle is depreciated by $3150 per year.

Step 3 ：We can represent the value of the vehicle t years after purchase with a linear function of the form y=mt+b.

Step 4 ：Here, m represents the rate of depreciation per year, and b represents the initial value of the vehicle.

Step 5 ：So, m = -3150 (since the value is decreasing each year) and b = 31500 (the initial value of the vehicle).

Step 6 ：Substituting these values into the equation gives us the model for the value of the car t years after purchase: \(y = -3150t + 31500\).

Step 7 ：\(\boxed{y = -3150t + 31500}\) is the final answer.