You just wrote an equation to determine the height of the tree, y, after x years. What does this equation mean?

Question

x
y
(4, 120)(7, 150)
0
1
2
3
4
5
6
7
8
9
10
0
15
30
45
60
75
90
105
120
135
150
165
180
Number of years
Height (inches)
y= mx + b
y= 10x + 80

The tree was
inches when Stella planted it, and it grew
inches each year.

Answer 1

The equation you provided for the height of the tree \(y = 10x + 80\) represents a linear relationship between the height of the tree and the number of years since it was planted.

Here's the breakdown of the equation:

• \(y\) is the height of the tree in inches.
• \(x\) is the number of years since the tree was planted.
• The slope \(m = 10\) indicates that the tree grows 10 inches each year.
• The y-intercept \(b = 80\) indicates that when Stella planted the tree (when \(x = 0\)), the height of the tree was 80 inches.

Therefore, to summarize:

• The tree was 80 inches tall when Stella planted it, and it grew 10 inches each year.