To determine the slope of the line of best fit for the given data points, we can use linear regression analysis. In linear regression, the line of best fit is represented by the equation:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope of the line and [tex]\( b \)[/tex] is the y-intercept.
Given data points:
[tex]\[
x: [0, 1, 2, 2, 3, 5, 5, 7, 7, 9]
\][/tex]
[tex]\[
y: [2, 5, 2, 4, 7, 6, 5, 3, 9, 9]
\][/tex]
Using technology, we find that the slope of the line of best fit is approximately:
[tex]\[ 0.568 \][/tex]
Thus, among the given options:
1. The slope of the line is approximately -2.87.
2. The slope of the line is approximately -0.568.
3. The slope of the line is approximately 2.87.
4. The slope of the line is approximately 0.568.
The correct answer is:
[tex]\[ 0.568 \][/tex]
