Janet is training for a marathon. She decides to track her time per mile, in minutes, for 8 weeks. Which equation best fits the data?

A graph is labeled as Marathon Training. The horizontal axis is labeled as Weeks and the vertical axis is labeled as Time per mile left parenthesis minutes right parenthesis. The values on the horizontal axis range from 0 to 10 in increments of 2 and the values on the vertical axis range from 0 to 10 in increments of 2. Nine points are marked on the graph with their coordinates approximately equal to (0, 10), (1, 9 decimal point 9), (2, 9 decimal point 6), (3, 9 decimal point 5), (4, 9 decimal point 4), (5, 9 decimal point 2), (6, 9), (7, 8 decimal point 7), and (8, 8 decimal point 6).

A. y=0.18x + 10.06
B. y=−0.18x + 10.06
C. y = 2x + 8.6
D. y = −2x + 8.6

To find the line that best fit the data is to substitute the values in this equation [tex]y=a x+b[/tex] where [tex]a=\frac{\left(N * \sum x y\right)-\left(\sum x * \sum y\right)}{\left(N * \sum x^{2}\right)-\left(\sum x * \sum x\right)}[/tex] and [tex]b=\frac{\left(\sum x^{2} * \Sigma y\right)-\left(\sum x * \Sigma x y\right)}{\left(N * \Sigma x^{2}\right)-\left(\sum x * \Sigma x\right)}[/tex]

Using the values from the table attached below, we can substitute and find the values of a and b

Substituting the values of a, we get,

[tex]\begin{aligned}a &=\frac{\left(N * \sum x y\right)-\left(\sum x * \Sigma y\right)}{\left(N * \sum x^{2}\right)-\left(\sum x * \sum x\right)} \\&=\frac{(9 * 324.9)-(36 * 83.9)}{(9 * 204)-(36 * 36)} \\&=-0.18\end{aligned}[/tex]

Similarly, substituting the values of b, we get,

[tex]\begin{aligned}b &=\frac{\left(\sum x^{2} * \Sigma y\right)-\left(\sum x * \sum x y\right)}{\left(N * \sum x^{2}\right)-\left(\sum x * \sum x\right)} \\&=\frac{(204 * 83.9)-(36 * 315)}{(9 * 204)-(36 * 36)} \\&=10.06\end{aligned}[/tex]

Thus, substituting the values of a and b in the formula, we get,

[tex]\begin{aligned}y &=a x+b \\&=-0.18 x+10.06\end{aligned}[/tex]