A scientist is studying red maple tree growth in a state park. She measured the trunk diameters of a sample of trees in the same month every other year. The tables show the data for two of the trees.

\begin{tabular}{|r|c|}
\hline \multicolumn{2}{c}{ Tree 1 } \\
\hline Year & \begin{tabular}{c}
Trunk \\
Diameter \\
(inches)
\end{tabular} \\
\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{tabular}

\begin{tabular}{|r|c|}
\hline \multicolumn{2}{c|}{ Tree 2 } \\
\hline Year & \begin{tabular}{c}
Trunk \\
Diameter \\
(inches)
\end{tabular} \\
\hline 1 & 11.4 \\
\hline 3 & 12.0 \\
\hline 5 & 12.6 \\
\hline 7 & 13.2 \\
\hline 9 & 13.8 \\
\hline 11 & 14.4 \\
\hline 13 & 15.0 \\
\hline
\end{tabular}

The scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. Complete a linear equation that fits the data for Tree 1, where [tex]\(x\)[/tex] is the year and [tex]\(y\)[/tex] is the trunk diameter, in inches. Click on the variables and numbers you want to select and drag them into the boxes.

Equation for Tree 1: [tex]\(y = mx + b\)[/tex]

Available options:

- [tex]\(-0.6\)[/tex]
- [tex]\(-0.3\)[/tex]
- 0.3
- 0.6
- 18.0
- 18.3
- 18.6

[tex]\(\rightarrow\)[/tex]



Answer :

To create a linear equation that models the data for Tree 1, where [tex]\( x \)[/tex] is the year and [tex]\( y \)[/tex] is the trunk diameter in inches, we first identify the slope ([tex]\( m \)[/tex]) and the y-intercept ([tex]\( b \)[/tex]) of the equation of the form:

[tex]\[ y = mx + b \][/tex]

Based on the data for Tree 1, the slope ([tex]\( m \)[/tex]) is approximately 0.3, and the y-intercept ([tex]\( b \)[/tex]) is approximately 18.3.

Thus, the linear equation that fits the data for Tree 1 is:

[tex]\[ y = 0.3x + 18.3 \][/tex]

This equation can now be used to predict the trunk diameter of Tree 1 in future years.