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."
Let's assume the height of the Oak tree is represented by the equation y = 0.5x + 2 and the height of the Pine tree is represented by the equation y = 0.75x.
For the Oak tree:
- Slope (m) = 0.5, which represents the rate at which the height of the Oak tree increases each year.
- Intercept (b) = 2, which represents the initial height of the Oak tree.
For the Pine tree:
- Slope (m) = 0.75, which represents the rate at which the height of the Pine tree increases each year.
- Intercept (b) = 0, as there is no initial height offset given in the problem.
To determine when the two trees were the same height, we can set the two equations equal to each other:
0.5x + 2 = 0.75x
Solving for x:
2 = 0.25x
x = 8
Therefore, the two trees were the same height after 8 years.