The value of a car decreases at a constant rate as it grows older. When the car is 2 years old, it is worth $23,000. When the car is 5 years old it is worth $15,500.

so you are looking for a linear relation in the form y = mx + b

where you are given two points
(2,23000) and (5,15500)
so slope = (15500-23000)/(5-2)= 7500/3
= -2500

so y = -2500x + b
sub in the first point
23000 = -2500(2) + b
b = 28000

finally :
y = -2500x + 28000

how did you get b= 28000

No, the equation that relates the value of the car (y) to the age of the car (x) is given by:

y = mx + b

Where:
m is the rate at which the value decreases per year.
b is the initial value of the car when it is new.

To find the rate of decrease (m), we can use the given information that when the car is 2 years old, it is worth $23,000, and when the car is 5 years old, it is worth $15,500.

Using the point-slope form of a linear equation:

m = (y2 - y1) / (x2 - x1)

Substituting the values:

m = (15,500 - 23,000) / (5 - 2)
m = -7,500 / 3
m = -2500

So the equation relating the value of the car (y) to the age of the car (x) is:

y = -2500x + b

To find the initial value (b), we can substitute one of the given points (x, y) = (2, $23,000) into the equation:

23,000 = -2500(2) + b
23,000 = -5000 + b
b = 23,000 + 5000
b = 28,000

Therefore, the equation relating the value of the car (y) to the age of the car (x) is:

y = -2500x + 28,000

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.