Question

in 1980, median family income was about $17,000 and in 2000 it was about $42,000. A) find the slope of the line passing through the points (1980,17000) and (2000,42000). B) interpret the slope as a rate of change. C) if this trend continues, estimate the median family income in 2004.

Answer 1

@Jhannybean help please

Answer 2

for part a), use the slope formula

m = (y2-y1)/(x2-x1)

Answer 3

In this case, (x1, y1) = (1980, 17000), which means x1=1980 and y1=17000

and (x2, y2) = (2000, 42000), telling us that x2=2000 and y2=42000

Answer 4

Let's see.

slope is defined by \[m=\] ....i think jim's got this xD

Answer 5

so it would be m= 42000 - 17000
2000 - 1980

Answer 6

keep going

Answer 7

which becomes 25000
20

Answer 8

good, whats next

Answer 9

dont know now this is where I kept getting stuck at

Answer 10

well you can cancel off a 0 from each to get 2500/2

Answer 11

now either use a calculator or long division to get 2500/2 = ???

Answer 12

which will give me 1250

Answer 13

so that's your slope

Answer 14

what does it mean in this context here?

Answer 15

the first part does ask what m equals but now it asks if the income increases or decreases and if so if it does by year or between the years of 1980 and 2000

Answer 16

well it's $17,000 in the year 1980

and it turns into $42,000 in the year 2000

Answer 17

so you tell me

Answer 18

I know that it is increasing but I am not sure of yearly or just between them years

Answer 19

do you think the increase jumps from 17,000 to 42,000 in one big jump?

Answer 20

yearly

Answer 21

that's more realistic

Answer 22

and that's exactly what the slope is: the yearly change in median family income

Answer 23

m = 1250 means the median family income increases $1250 each year (roughly)

Answer 24

ok so now to figure out the income for 2004 I would just keep adding 1250 to the 42000 correct

Answer 25

you could

Answer 26

that's the long way to do it

Answer 27

1250 · 4

Answer 28

and it's kinda error prone if you don't keep track of everything

Answer 29

or you could find the equation of the line that goes through the two points first

Answer 30

then plug in x = 2004 to find y

Answer 31

oh i see what you mean, yeah that works

Answer 32

in 2004 the income will be 47000 am I correct?

Answer 33

4*1250 = 5000

so adding 5000 to the income in 2000 will give you the income in 2004

Answer 34

correct

Answer 35

ok thank you so much

Answer 36

yw