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.

Write and equation relating y (value of the car $) to x (age of car).

this is just like the other one. The car dropped in value by $7500 in 5 years.

That is $1500/year, so the slope of the line

y = mx+b is -1500

That means

y = -1500x + b

Now you just have to find b so it fits the data.

To write an equation relating the value of the car ($y) to the age of the car (x), we can use the concept of a linear function, since the value of the car decreases at a constant rate.

Let's denote the initial value of the car (when it is new) as "a" and the rate at which it depreciates per year as "m".

From the given information:
When the car is 2 years old, it is worth $23,000.
This gives us the point (2, 23000).

When the car is 5 years old, it is worth $15,500.
This gives us the point (5, 15500).

Using these two points, we can find the equation of the line.

The formula for a linear equation is:
y = mx + a

To find the equation, we need to find the values of "m" and "a".

First, let's find the rate of depreciation "m":
m = (y2 - y1) / (x2 - x1)
m = (15500 - 23000) / (5 - 2)
m = -7500 / 3
m = -2500

Now, let's substitute the value of "m" and one of the points (2, 23000) into the equation:
23000 = -2500(2) + a

Simplifying this equation gives us:
23000 = -5000 + a

To isolate "a", we add 5000 to both sides:
23000 + 5000 = a
a = 28000

Therefore, the equation relating the value of the car ($y) to the age of the car (x) is:
y = -2500x + 28000