Question 1024861: In 1980, the average price of a home in Lake County was $94,000. By 1987, the average price of a home was $129,000. Which of the following is a linear model for the price P of a home in Lake County, in terms of the year t? Let correspond to 1980.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! price of a home in 1980 is 94000
price of a home in 1987 is 129000
what is formula?
what is price of a home in 1990 based on this formula?
this is a linear equation.
the slope of the linear equation is (y2-y1)/x2-x1)
y2-y1 is 129000 - 94000 = 35000
x2-x1 is 1987 - 1980 = 7
slope of the equation is equal to 35000 / 7 which is equal to 5000.
the slope intercept form of a straight line equation is y = mx + b.
m is the slope.
b is the y-intercept.
your equation starts off as y = 5000 * x + b.
use one of your data points to solve for b.
one data point is x1 = 0 and y1 = 94000.
y = 5000 * x + b becomes 94000 = 5000 * 0 + b.
this results in b = 94000.
your equation of y = 5000 * x + b becomes y = 5000 * x + 94000.
the slope is 5000.
the y-intercept is 94000.
when x = 0, the year is 1990,
when x = 7, the year is 1987.
the year 1990 is 3 years from the year 1987, therefore .....
when x = 10, the year is 1990.
solve the equation for x = 10 and you get the projected value of a home in 1990.
that value would be y = 5000 * 10 + 94000 which becomes y = 144000.
the graph of the equation of y = 5000 * x + 94000 is shown below, with the pertinent coordinates marked.
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