Year The House's Value example essay topic

In order to create a graph such as the one Ms. Red kin uses to calculate the depreciation of her rental house, first it must be determined which part of the information given is the dependant variable and which is the independent variable. In this case the independent variable is time (in years), and the dependent the value of the house. Next create a graph with the given data, the independent variables on the x-axis and the dependent on the y. Graph and label the given data as points (4 yrs, $64000) and (7 yrs, $52000), allow the graph to represent the house's value from when it was new to 10 years after its purchase. Graph a line from these two points, now you may follow the line to find the approximate value of the house at certain years of depreciation.

In order to find the value of the rental house after ten years, follow the line previously graphed to 10 on the x-axis. The y value you should receive should be 40,000, and if you were searching for the value of the house when it was new, the graph shows $80,000 at 0 years. Another example of how this graph may be used is in finding which year the house reaches a certain value. In order to find out which year the house's value becomes 55,000 follow the graphed until you come upon the value of 55,000. The x value associated with the value 55,000 is 5 years, so the answer is the rental house will depreciate in value to 55,000 at 5 years. The slope of the line will be required to find many other answers to questions you may have concerning the house and its depreciation.

To determine the slope of the line, use the given points of (4, 64000) and (7, 52000) in the equation (y 2-y 1) / (x 2-x 1), that is determine the change in y divided by the change in x which is the slope. (52000-64000) / (7-4) is the specific equation we will need for this line, the solution, -4000 is the slope of the line once simplified. One way to use the slope is to formulate an equation which will relate the value of the house to the number of years depreciated. Let V stand for the value, and t stand for the number of years it has been depreciated. To complete this equation we will also need to know the y intercept so we may use the equation y = mx + b. To find the y intercept, use the two point program on your graphing calculators, with the points provided in the given data.

This will also provide an opportunity to check the slope of the equation, the correct answers should be m = -4000 y intercept = 80,000. Now follow the slope intercept equation format to create an equation to determine the value of the house relating to the time in years it has been depreciated. Following slope-intercept notation the equation should be V (t) = -4000 (t) + 80,000. To put this equation to use, again seek the price of the house when it was new. Using the equation V (0) = -4000 (0) +80,000 we find the value of the house brand new was 80,000. Also we may check our answer we derived from the graph for the value of the house at 10 years with the same equation, replacing t with 10.

V (10) = -4000 (10) + 80,000: The solution is 40,000. The same answers may be derived from either method, using a line to find graphical solutions, or by using an equation. These methods are interchangeable and should provide you with the same answers..