SOLUTION: Can you help me solve this word problem?
Your property tax is based on the assessed value of your property.(The assessed value is often lower than the actual value of the proper
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Question 323739: Can you help me solve this word problem?
Your property tax is based on the assessed value of your property.(The assessed value is often lower than the actual value of the property.) A house that has an assessed value of $150,000 has a property tax of $5520.
(a) Find the mathematical model that gives the amount of the property tax y in terms of the assessed value x of the property.
(b) Use the model to find the property tax on a house that has an assessed value of $185,000.
I think I have to use y-y1=m(x-x1) for this equation, but I am not real sure. I do not know where to began. This is what I have thus far 150,000-y = m(x-5520)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Assessed Value of the Property is $150,000
Property Tax is $5,520.
Property Tax Rate is 5,520/150,000 = .0368 for each dollar of assessed value.
Multiply that by 1000 to get 36.8 for each one thousand dollars of assessed value.
On the house with an assessed value of $150,000, the property tax is calculated as either .0368 * 150,000 or 36.8 * 150.
The .0368 * 150,000 is using property tax rate for each dollar of assessed value.
The 36.8 * 150 is using property tax rate for each one thousand dollars of assessed value.
Both will get the same property tax.
.0368 * 150,000 = 5,520
36.8 * 150 = 5,520
Now that you know the property tax rate, you can apply it to another house of a different value.
If the assessed value of the other house is $185,000, then the property tax is calculated to be:
.0368 * 185,000 = $6,808.
It can also be calculated to be:
36.8 * 185 = $6,808.
Either way you get the same tax rate..
In terms of an equation that you can graph, you would set the property tax equal to y and you would set the assessed value of the house equal to x.
Your equation would be either:
y = .0368 * x
or:
y = 36.8 * x
The difference between these graphs is in the range of x.
In the first graph x value is from -200,000 to 200,000
In the second graph x value is from -200 to 200
In the firs graph, each unit of x represents one dollar.
In the second graph, each unit of x represents one thousand dollars.
The graph of y = .0368 * x would look like this:
The graph of y = 36.8 * x would look like this:
These graphs are identical.
The only difference is that the values of x are much easier to see in the second graph than in the first graph.
What I think you tried to do was to make a straight line equation out of the values.
That's ok, except that you needed to get the following:
Straight line equation is y = mx + b where m is the slope.
The slope of the equation is equal to (y2-y1) / (x2-x1)
You needed 2 values of y and 2 values of x.
You were given the value of x1 as $150,000.
You were given the value of y1 as $5,520.
From that you needed to calculate the tax rate which was $5,520 / $150,000 which was equal to .0368.
You were then told to find the property tax for $185,000.
That tax was $6,808.
You now have y2 = $6,608 and x2 = $185,000
So far you have:
x1 = $150,000
y1 = $5,520
x2 = $185,000
y2 = $6,808
From those values you can find the equation of the straight line.
The slope of that equation would be:
(y2-y1)/(x2-x1) = $6,808 - $5,520) / ($185,000 - $150,000) = $1,288 / $35,000 = .0368.
The slope of your line is .0368.
Since the slope intercept form of a straight line is y = mx + b and the slope is equal to m, then m = .0368 and the equation becomes:
y = .0368 * x + b
You now want to find the y-intercept of this equation.
You do that by substituting one of the (x,y) pairs that you already have.
Let's use (x1,y1) which equals (150,000,5,520).
Using that pair of (x,y) values, your equation now becomes:
5,520 = .0368 * 150,000 + b
Now you need to solve for b.
Subtract .0368 * 150,000 from both sides of the equation to get:
5,520 - .0368 * 150,000 = b.
Simplify to get:
5,520 - $5,520 = b which results in:
b = 0.
The equation of your straight line is y = .0368 * x.
this means that when x is equal to 0, the value of y = 0.
With this equation, the y values are in units of one dollar each and the x values are in units of one dollars each.
To make the x values in units of one thousand dollars each, we need to multiply this equation by 1000 on the right hand side to get:
y = 36.8 * x
y is still in units of one dollar each. x is now, however, in units of one thousand dollars each.
If the conversions for graphing purposes throw you, then disregard them.
The answer to your question is:
The tax rate is .0368 for each dollar of assessed value.
The tax rate for a house assessed at $150,000 = .0368 * $150,000 = $5,520.
The tax rate for a house assessed at $185,000 = .0368 * $185,000 = $6,808.
The equation in terms of x and y is y = .0368 * x, where y is the property tax and x is the assessed value of the house and .0368 is the tax rate.
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