<Student’s name>
<University>
Well, from a certain resource we know, that the property tax on a home and the assessed value of the home are linearly related to each other. Generally, linear relationship between two variables means that the degree of change of one variable on one unit involves the change of the other on some constant value (usually it is named “k”). In this case, one variable is a property tax (called “t”) and the other variable is the assessed value of the home (called “v”). As these variables are directly proportional (so, they are linearly related to each other), hence, we can write down the formula of relationship:
t=k∙v
So, we can take some certain assessed value of the home, multiply it on a coefficient k, and we will get the related property tax amount. It is naturally that k is a property tax rate (in %).
The purpose of our solution is to determine this tax rate (k-value). Given that when the assessed value of the home is $140,000 the amount of property tax (in money) is $2100. Hence,
2100=k∙140000
As we know, for each v value there is exists a corresponding t value. It will be different depending on different v values. But k is always constant. That’s why we can find the tax rate k. For this we express k from the last equation:
k=2100140000=0.015
The obtained value has the following interpretation: the property tax rate is 1.5% of the assessed value of a home.
The equation now has a form:
t=0.015∙v
Now, when we know the tax rate, we can evaluate a property tax in money for any home. In our case, the question is to find what is the property tax on a home with the assessed value of $180,000? For this we must substitute 180000 as v value, and, knowing k, just compute the corresponding t value:
t=0.015∙180000=2700
The solution has the following interpretation: the amount of a property tax for the home with assessment value of $180,000 is $2,700.
This example demonstrates us the subject of linear relationships very clearly.
