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 will use the equation:
y = 3x + 2
The slope (m) of 3 represents the rate at which the Oak tree is growing each year.
To graph the Pine tree, we will use the equation:
y = 2x + 6
The slope (m) of 2 represents the rate at which the Pine tree is growing each year.
To determine when the two trees were the same height, we can set the two equations equal to each other:
3x + 2 = 2x + 6
And solving for x gives:
x = 4
Therefore, the two trees were the same height at year 4.