Linear equations and models

[travel]

I know that I have made a mistake somewhere because my answer doesnt make sense, but I am not sure where.
The percentage of female smokers in the US declines from 21% in 2000 to 18% in 2006. Find a linear model relating the percentage f of female smokers to years t since 2000. Use the model to predict the frist year for which the % offemale smokers will be less that or equal to 10%.
I began with the y=mx+b formula but switched the letters to f=mt+b
I figured out tht m=-1/2 using rise over run to find the slope
Rise being the y values 21-18 and Run being the x values of 2000-2006
So my ordered pairs would be (2000,21) (18,2006)
When I plug in one set of order pairs into the eqation I dont produce a answer that mkes sense.
18=-1/2(2006)+b = b=1021

 

[mmm4444bot]

years t since 2000

The key word in this phrase is "since".

In 2000, t = 0

In 2001, t = 1

In 2002, t = 2

In 2003, t = 3

et cetera

In other words, the independent variable t counts the number of elapsed years (since the year 2000).

So my ordered pairs would be (2000,21) (18,2006)

The order is wrong, in the pair (18, 2006). We always list the independent variable first and the dependent variable second.

In other words, we write (x, y) or (t, f).

You wrote (y, x) or (f, t), which is not correct.

Aside from these mistakes, your reasoning seems correct.

 

[fmbeach]

The first comment is correct, 2000= time zero and 2006 = time 6.
That will give you b=21, which should have been obvious if you had thought of 2000 as time zero.
(0, 21) and (6, 15) are your points. Now you can finish.