Question

The (average) sales price for single family property in Seattle and Port Townsend is tabulated below.



Year Seattle Port Townsend


1970 $38,000 $8,400


1990 $175,000 $168,400



Find a linear model relating the year x and the sales price y for a single family property in Seattle.

Answer 1

Answer:

$y=6,850x - 13,456,500$

Step-by-step explanation:

To find the linear model, we need to find a linear equation, where its slope is defined as

$m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

So, we use the given points (1970, 38000) and (1990, 175000), to find the slope

$m=\frac{175,000-38,000}{1990-1970}=\frac{137,000}{20} =6,850$

Now, we use the point-slope formula to find the equation

$y-y_{1} =m(x-x_{1} )\\y-38000=6850(x-1970)\\y=6850x-13,494,500+38,000\\y=6,850x - 13,456,500$

Therefore, the linear model is

$y=6,850x - 13,456,500$