For this final problem, you are tasked with the following: write down the equations you used to graph each tree in problem #2, and then state what each slope represents from each equation in y=mx+b
form.
Here is the previous question for reference:
"Brittany buys two trees for her backyard, one Oak tree and one Pine tree. She plants them appropriately and measures their initial height. Every year Brittany measures the height of the two trees and eventually realizes that the two trees must have had the same height at some point! Construct two linear equations in the form ,y=mx+b
from the table and determine when the trees were the same height. "
Year Oak Pine
0 2 6
1 5 8
2 8 10
To graph the Oak tree, we can use the points (0,2), (1,5), and (2,8) to create the equation:
y = 3x + 2
In this equation, the slope (m) of 3 represents the rate at which the Oak tree is growing each year.
To graph the Pine tree, we can use the points (0,6), (1,8), and (2,10) to create the equation:
y = 2x + 6
In this equation, the slope (m) of 2 represents the rate at which the Pine tree is growing each year.
To find out when the two trees were the same height, we can set the two equations equal to each other:
3x + 2 = 2x + 6
3x - 2x = 6 - 2
x = 4
Therefore, the two trees were the same height at year 4.