Posted: 11/22/2007 10:52:28 AM EDT
If the market value of the property at 20% affordable is $50,000, and the value at 47% affordable is $31,000, then the value at 80% affordable should be 
|
This is not simply an algebra problem. I'm good through calc I, math-wise, but I have no idea what "20% affordable" and "47% affordable" mean - is that a real estate term? For the purposes of this problem, I will assume that the affordability rate is linear - since the question only gives two plot points, that's the only way to answer it. A straight line in the cartesian coordinate system is defined by its slope and y-axis intercept: Y = mX + b [m is slope, b is intercept] The slope is the ratio of the change in Y to the change in X. Here, your question gives us the plot points of (20%, 50K) and (47%, 31K). So (20-47)/(50-31), or -27/19, is your slope. So far, our line is defined as Y = (-27/19)X + b. To find the intercept, we can now plug in one of our plot points to the working line definition: 50K = (-27/19)20 + b. Multiplying, we get 50K = (-380/27) + b. Isolating the intercept, we get 50K + 380/27 = b. So b = 17330/27. Now we have a complete definition of our line: Y = (-19/27)X + 1730/27 Finally, just plug in 80 for X to find your answer: Y = (-19/27)80 + 1730/27. Y = -1520/27 + 1730/27. Y = (-1520+1730)/27. Y = 210/27. Y = 7 21/27, or roughly $7,778. The value at 80% affordable is $7,778. |
