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

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

Explanation:

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

`m=(y_(2) -y_(1) )/(x_(2)-x_(1) )`

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

`m=(175,000-38,000)/(1990-1970)=(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`