No, the equation y - 23,000 = -2500x - 5 is not correct. Let me explain how we can find the correct equation.
First, let's identify the given information:
- When the car is 2 years old, it is worth $23,000.
- When the car is 5 years old, it is worth $15,500.
To write an equation relating the value of the car (y) to the age of the car (x), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
We know that the value of the car decreases at a constant rate as it grows older. So, we can determine the slope by finding the change in value (Δy) divided by the change in age (Δx).
The change in value is $15,500 - $23,000 = -$7,500, and the change in age is 5 - 2 = 3. Dividing the change in value by the change in age, we get:
m = Δy / Δx = -7500 / 3 = -2500
Now we have the value of the slope (m = -2500). To find the y-intercept (b), we can substitute the values of a known point (x, y) into the equation. We can use either (2, 23000) or (5, 15500) since both points are given. Let's use (2, 23000):
y = mx + b
23000 = -2500(2) + b
23000 = -5000 + b
b = 23000 + 5000
b = 28000
Now we have the slope (m = -2500) and the y-intercept (b = 28000), so we can write the equation relating y to x:
y = -2500x + 28000
Therefore, the correct equation relating the value of the car (y) to the age of the car (x) is y = -2500x + 28000.