Find a linear model and use it to make a prediction.?

Question

There are 55 blades of grass in 1 in.^2 of lawn. THere are 230 blades of grass in 4in.^2 of the same lawn. How many blades of grass are in 3 in.^2 of lawn?

Answer 1

Hi,
1) Calculate the slope:
m = (230-55)/4-1)
= 175/3
2) Now we solve for "b" in the linear equation y = mx +b.
g = (175/3)A +b (where g = number of blades of grass.)
230=(175/3)(4) +b
230 -700/3 = b
-3.333 = b

So, our equation is:
g = (175/3)A - 3.3333
Now, calculate the number of blades of grass is 3 in².
g = (175/3)(3) -3.3333
= 175 -3.3333
=171.67
or since blades of grass don't come in decimals, 172 blades.

Hope this helps.
FE