help question in description

Question

In 1990 the average family income was about 38000, and in 2000 it was about 62308.Let  represent 1990,  represent 1991, and so on. Find values for  and  (rounded to one decimal place if necessary) so that  models the data

a=

b=

What was the average family income in 1995?

_________

Answer 1

X1=0, y1=38000,

X2=10, y2=62308

ax+b=y

a= (y2-y1) / (x2-x1) =24308/10 = 2430.8

Use ax+b=y @ x1=0, y1 = 38000 to find b

b = 38000

2430.8x+38000=y

Answer 2

Hi Leon,

Basically, this prompt is asking you to find an equation where the points of (0, 38000) and (10, 62308) in the format (x,y) (NOTE we use x=0 as the same as x=1990 because of the instructions in the prompt, also F(x) is the same as y) are on the line, and then use that equation to solve for 1995.

To start, we use the a= (y2-y1)/(x2-x1) equation to solve for a, since this is a linear equation finding the distance between the two points will find a slope

the points we have are (0,38000) and (10, 62308),

thus (62308-38000)/(10-0);

(30308/10) or 3030.8=a

Next, we plug in a at a point to find b.

38000=3030.8(0)+b,

b=38000 (since x=0, finding b is easy when given a y value when x=0; this is the same as the y intercept concept)

Finally, we can solve for y when x=1995 (or 5) by combining the values of a and b in the y=ax+b;

y=(3030.8)(5)+38000;

y=15154+38000

y=53154.

If there is any point where you would like a deeper explanation on why this is the best method, please feel free to contact me at [email protected]