High School Math question?

Use height y = m*x + b

Rate of growth/year m = (41-36)/(6-4) = 5/2 = 2.5"/year = m

Now find b

36" = 4yr*2.5inch/yr + b  =====> b = 26"

Verify

41" = 6yr*2.5inch/yr + 26 = 15 + 26" = 41" checks

Height = 9yr*2.5in/yr + 26 = 45/2 + 26 = (45+52)/2 = 48.5" <<<<<

So, first we need to determine the girl's rate of growth. The units we're working with here are inches and years, so we need to determine how many inches per year the girl grows.

First we find the difference between her height in inches at ages 4 and 6 - "difference" means subtraction, so we subtract 36 from 41 and get 5. Her height has changed by that many inches.

We know that the difference in age from one measurement to the next is two years, because we know that 6 minus 4 is 2 (and 4 plus 2 is 6). So, now we have our values. 

Inches = 5, years = 2. 

And we know that a rate can be expressed as a fraction, which is really just division written funny. 5/2, or 5 divided by 2, is 2.5. Growing 5 inches in 2 years is the same as growing 2.5 inches in 1 year. We can check that by doing it backwards, because we know that division and multiplication are opposites - 2.5 times 2 is 5. So, her average rate of growth is 2.5 inches per year.

If we assume she continues growing at that rate of 2.5 inches every year, then from here it should be dead easy to figure out how tall she'll be by age 9.

We could just count (41 plus 2.5 is 43.5 inches at age 7, plus 2.5 is 46 inches at age 8, plus 2.5 is 48.5 inches at age 9), but we can also multiply, which is really just fast counting. 

We'll take our rate of 2.5 inches times the number of additional years beyond the starting age (which is 5, 9 minus 4 is 5) and add that to the starting height of 36". 5 times 2.5 is 12.5, plus 36 is 48.5 inches tall by age 9. It would also work if we multiplied 2.5 by the number of additional years beyond age 6 (which is 3, 9 minus 6 is 3), and added that to the height at age 6 (3 times 2.5 is 7.5, plus 41 is 48.5).

We can express what we've done here algebraically with the following equation, where H is the girl's height in inches and A is her age in years, using the starting point of 36 inches tall at age 4.

H = 36 + (2.5 * (A-4))

(41-36) /2= rate of growth    

(Rate of growth *3)+41 = answer