To determine which equation best approximates the line of best fit of Raquel's darts, we can follow these steps:
1. Extract Coordinates: Identify the given dart coordinates on the grid:
- [tex]\((-5, 0)\)[/tex]
- [tex]\((1, -3)\)[/tex]
- [tex]\((4, 5)\)[/tex]
- [tex]\((-8, -6)\)[/tex]
- [tex]\((0, 2)\)[/tex]
- [tex]\((9, 6)\)[/tex]
2. Calculate the Line of Best Fit:
We will use a statistical method like Linear Regression to calculate the line that best fits these points. The line of best fit is given by the equation [tex]\( y = mx + c \)[/tex] where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( c \)[/tex] is the y-intercept of the line.
3. Extract [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values: Separate the coordinates into [tex]\( x \)[/tex] and [tex]\( y \)[/tex] components:
- [tex]\( X = [-5, 1, 4, -8, 0, 9] \)[/tex]
- [tex]\( Y = [0, -3, 5, -6, 2, 6] \)[/tex]
4. Fit the Linear Model: Use a technique (like least squares) to fit a line to these points to find the values of [tex]\( m \)[/tex] and [tex]\( c \)[/tex].
5. Match the Line Equation:
Compare the calculated slope ([tex]\( m \)[/tex]) and intercept ([tex]\( c \)[/tex]) with the given options:
- [tex]\( y = 0.6x + 0.6 \)[/tex] where [tex]\( m = 0.6 \)[/tex] and [tex]\( c = 0.6 \)[/tex]
- [tex]\( y = 0.1x + 0.8 \)[/tex] where [tex]\( m = 0.1 \)[/tex] and [tex]\( c = 0.8 \)[/tex]
- [tex]\( y = 0.8x + 0.1 \)[/tex] where [tex]\( m = 0.8 \)[/tex] and [tex]\( c = 0.1 \)[/tex]
- [tex]\( y = 0.5x + 0.6 \)[/tex] where [tex]\( m = 0.5 \)[/tex] and [tex]\( c = 0.6 \)[/tex]
By going through this process, we find that the best fit for the line given Raquel's dart coordinates corresponds to the equation:
[tex]\[ y = 0.6x + 0.6 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
