Patty buys a new car and gets it appraised every few years. After owning the car for 3 years, it’s value is $15,000. After owning the car for 5 years, it’s value is $9,000. What is the constant of proportionality in this inverse variation?

The constant of proportionality in the inverse variation is -3000

Step-by-step explanation:

Given that the initial value of the car was X, after owning the car for 3 years the value is $15,000 and the value after 5 years was $9,000 we have;

At  year 3, value of car = $15,000

At year 5, value of car = $9,000

Rate of change of car value with time = Constant of proportionality

Rate of change of car value with time = (15000 - 9000)/(3 - 5) = -3000

The constant of proportionality = -3000

Therefore;

y - 15000 = -3000 × (x - 3)

y = -3000x + 9000 + 15000 = -3000·x + 24000  

The value of the car, y with time,x is, y = -3000·x + 24000

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.