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Sagot :
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.
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.
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