Let's go through the steps to complete the linear equation that models the data for Tree 1.
We have the data for Tree 1:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Year} & \text{Trunk Diameter (inches)} \\
\hline
1 & 18.6 \\
\hline
3 & 19.2 \\
\hline
5 & 19.8 \\
\hline
7 & 20.4 \\
\hline
9 & 21.0 \\
\hline
11 & 21.6 \\
\hline
13 & 22.2 \\
\hline
\end{array}
\][/tex]
To find the linear equation [tex]\( y = mx + b \)[/tex], where:
- [tex]\( y \)[/tex] is the trunk diameter,
- [tex]\( x \)[/tex] is the year,
- [tex]\( m \)[/tex] is the slope of the line, and
- [tex]\( b \)[/tex] is the y-intercept.
From our calculations, we have:
- The slope [tex]\( m \)[/tex] = 0.3
- The y-intercept [tex]\( b \)[/tex] = 18.3
Hence, the linear equation is:
[tex]\[
y = 0.3x + 18.3
\][/tex]
So, the completed equation for Tree 1 is:
[tex]\[
y = 0.3x + 18.3
\][/tex]
This equation can be used to predict the trunk diameter in the future based on the year.
