In 1980, the median family income was about $16,000 and in 2000 it was $42,000. Find the slope of the line passing through the points (1980, 1600) (2000, 42,000). Interpret the slope as a rate of change. If this trend continues, estimate the median income for 2005.

Question

campbell_st · Answer

so the slope will need the data points (1980, 16,0000) and (2000, 42,000)

so the slope is m =  (42000 -16000)/(2000 - 1980)

anonymous · Answer

m=(260000) (20) ?

campbell_st · Answer

thats correct... so the m = 1300

and I had 1 to many zeros ..1st data point is (1980, 16000)

anonymous · Answer

i'm confused lol

campbell_st · Answer

ok... the data points you will use are

(1980, 16000) and (2000, 42000)

is that ok...

anonymous · Answer

yes

campbell_st · Answer

so the slope is 

42000 -16000)/(2000 -1980) = 26000/20

so the slope value is m = 1300 

is that ok...

anonymous · Answer

where do u get the 1300?

anonymous · Answer

nvm...I see now

campbell_st · Answer

26000/20 = 2600/2 = 1300

you can check it with a calculator

anonymous · Answer

i see it. thanks.

campbell_st · Answer

so this means that the average family income increases by $1300 per year...

does that make sense..?

anonymous · Answer

ok

anonymous · Answer

how do u know it's per year?

campbell_st · Answer

you are the change in money over time... year 2000 - year 1980 = 20 years... 

so the change is $26000 over 20 years or $1300 per year

anonymous · Answer

oh, i see. so do i find the median income for 2005 by adding 1300 per year to 2005 (to get 2005's amount) then add the three and divide by 3?

anonymous · Answer

wait, that's for finding an average isn't it? duh!

campbell_st · Answer

to get the value for 2005

use the information for 2000

so  

$$42000 + 5 \times 1300 $$

hope this makes sense.

anonymous · Answer

i got 10700, but i'm not sure how to figure it out myself.

anonymous · Answer

42000 (2000's income) + 5 (2005, add five more years) x 1300 (rate of increase per year)?

campbell_st · Answer

ummm... I think when they say ".. if the trend continues.." means that you are looking at a linear relationship... so the slope will be the same... 

so an easy way to do this is to use income for 2000 and add 5 years worth of $1300

so 

42000 + 5 x 1300 = $48 500

anonymous · Answer

48500

campbell_st · Answer

correct..

anonymous · Answer

i see!! thanks. wanna help with another one? :)

campbell_st · Answer

sorry... I have to go... there are plenty or people here to help... 

good luck

anonymous · Answer

ok, thanks for your help!