To find the line of best fit for the given data, we need to calculate the slope and y-intercept of the line that best represents this data. Here’s a step-by-step solution to determine the line of best fit:
1. List the given data:
[tex]\[
\begin{array}{|c|c|}
\hline x & y \\
\hline 2 & 2.9 \\
\hline 3.5 & 2 \\
\hline -1.4 & 4.8 \\
\hline 4.2 & 1.5 \\
\hline 0 & 4 \\
\hline -2.8 & 6 \\
\hline 1.5 & 3.5 \\
\hline
\end{array}
\][/tex]
2. Calculate the slope ([tex]\( m \)[/tex]) and y-intercept ([tex]\( b \)[/tex]) for the line of best fit.
The calculated slope and y-intercept for this data set are:
[tex]\[
\text{slope} = -0.613
\][/tex]
[tex]\[
\text{intercept} = 4.142
\][/tex]
3. Construct the equation of the line of best fit.
Using the slope ([tex]\( m \)[/tex]) and y-intercept ([tex]\( b \)[/tex]), we can form the equation of the line:
[tex]\[
y = -0.613x + 4.142
\][/tex]
4. Determine the best fit equation from the provided options:
We compare the constructed equation with the provided options:
- [tex]\( y = 0.613x - 4.142 \)[/tex]
- [tex]\( y = -0.613x - 4.142 \)[/tex]
- [tex]\( y = 0.613x + 4.142 \)[/tex]
- [tex]\( y = -0.613x + 4.142 \)[/tex]
The correct form that matches [tex]\( y = -0.613x + 4.142 \)[/tex] is the last option.
Result:
The best fit equation for the given set of data is:
[tex]\[
y = -0.613x + 4.142
\][/tex]
