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
0
Oak
2
1
5
2
8
Pine
6
8
10
10
Now we will answer the original question from the graph above! After _____ years the height of the trees are the same. When both trees measure the same height they ______ feet tall.
To construct two linear equations, we first need to find the slope and y-intercept for each tree.
For the Oak tree:
Using the points (0, 2) and (2, 8):
Slope = (8-2) / (2-0) = 3
Using the point (0, 2) and the slope:
y = 3x + 2
For the Pine tree:
Using the points (0, 6) and (2, 10):
Slope = (10-6) / (2-0) = 2
Using the point (0, 6) and the slope:
y = 2x + 6
To determine when the trees were the same height, we set the two equations equal to each other and solve for x:
3x + 2 = 2x + 6
x = 4
After 4 years, the height of the trees are the same. When both trees measure the same height they are 14 feet tall.