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Raquel throws darts at a coordinate grid centered at the origin. Her goal is to create a line of darts. Her darts actually hit the coordinate grid at [tex]\((-5, 0), (1, -3), (4, 5), (-8, -6), (0, 2)\)[/tex], and [tex]\((9, 6)\)[/tex]. Which equation best approximates the line of best fit of the darts?

A. [tex]\(y = 0.6x + 0.6\)[/tex]
B. [tex]\(y = 0.1x + 0.8\)[/tex]
C. [tex]\(y = 0.8x + 0.1\)[/tex]
D. [tex]\(y = 0.5x + 0.6\)[/tex]



Answer :

GinnyAnswer
To find the equation of the line of best fit for Raquel's darts, we will perform a linear regression on the given coordinates. Raquel's darts hit the coordinate grid at the following points:
[tex]\[ (-5, 0), (1, -3), (4, 5), (-8, -6), (0, 2), (9, 6) \][/tex]

The general form of the equation for a line is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

Through computation, the slope ([tex]\( m \)[/tex]) of the line and the y-intercept ([tex]\( b \)[/tex]) have been determined to be:
[tex]\[ \text{slope (} m\text{)} = 0.6333630686886709 \][/tex]
[tex]\[ \text{intercept (} b\text{)} = 0.561106155218555 \][/tex]

Thus, the equation of the line of best fit is:
[tex]\[ y \approx 0.633x + 0.561 \][/tex]
When we compare this with the given options:

1. [tex]\( y = 0.6x + 0.6 \)[/tex]
2. [tex]\( y = 0.1x + 0.8 \)[/tex]
3. [tex]\( y = 0.8x + 0.1 \)[/tex]
4. [tex]\( y = 0.5x + 0.6 \)[/tex]

The equation that best approximates our calculated line of best fit is:
[tex]\[ y = 0.6x + 0.6 \][/tex]

Hence, the equation that best approximates the line of best fit of Raquel's darts is:
[tex]\[ y = 0.6x + 0.6 \][/tex]

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