Use the information .." *In 1986, the population was 37200 people. In 1994, it was 42000 people.*" to find the growth rate in this period, i.e.,

(42,000 -37,200)/8 = 4800/8=600

where 8 is the number of years from 1986 to 1994. This number, 600, is your m in the equation of a line like y=mx+b.

So, how do you find b?

We now that in 1986 the population is 37,200 and that x = 1986-1984 =2. Hence:

37,200 = 600*2+ b

from which we find b = 36,000. In this way we have found the equation we were after, i.e., :

**y = 600*x + 36,000**

where x is the number of years past 1984. So x=1 represents 1985, x=2 represents 1986, and so on.

Note that for x=10, i.e. in 1994, your linear equation gives a population of 600*10+36,000 = 42,000 which is exactly the number you were given for the population in 1994.