To find the linear function that best fits the given data points, we'll use the method of linear regression to determine the slope (m) and the intercept (b) of the line [tex]\( y = mx + b \)[/tex].
We are given the following data points:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 1 & 3 & 5 & 7 & 9 \\
\hline
y & 2 & 3 & 4 & 5 & 6 \\
\hline
\end{array}
\][/tex]
Using linear regression, the best fit line through these points is determined by calculating the slope (m) and the y-intercept (b) such that [tex]\( y = mx + b \)[/tex].
For the given data:
- The slope [tex]\( m \approx 0.5 \)[/tex]
- The intercept [tex]\( b \approx 1.5 \)[/tex]
Therefore, the linear function that best fits the data is:
[tex]\[
y = 0.5x + 1.5
\][/tex]
This is the equation of the linear fit to the given data points.
