To determine the equation for the line of best fit given Maleia's running data over six months, we need to follow these steps:
1. Plot the Months vs. Times:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Month} & \text{Time (minutes)} \\
\hline 1 & 46 \\
\hline 2 & 42 \\
\hline 3 & 40 \\
\hline 4 & 41 \\
\hline 5 & 38 \\
\hline 6 & 36 \\
\hline
\end{array}
\][/tex]
2. Find the Line of Best Fit:
The line of best fit is typically in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
3. Calculate the Slope and Intercept:
We've identified the slope ([tex]\( m \)[/tex]) and intercept ([tex]\( b \)[/tex]) for the line of best fit as follows:
- The slope ([tex]\( m \)[/tex]) is approximately [tex]\( -1.742857142857142 \)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is approximately [tex]\( 46.6 \)[/tex].
4. Form the Equation:
Using the calculated slope and y-intercept, we can now write the equation of the line of best fit:
[tex]\[
y = -1.74x + 46.6
\][/tex]
Given this, let's compare it with the provided options:
[tex]\[
\begin{align*}
&\text{Option 1: } y = -174x + 466 & \quad (\text{Incorrect}) \\
&\text{Option 2: } y = -1.74x + 36.2 & \quad (\text{Incorrect}) \\
&\text{Option 3: } y = 174x + 466 & \quad (\text{Incorrect}) \\
&\text{Option 4: } y = 1.74x + 36.2 & \quad (\text{Incorrect}) \\
\end{align*}
\][/tex]
Thus, none of the options exactly match the precise result [tex]\( y = -1.74x + 46.6 \)[/tex]. However, if the correct answer had to be chosen from the given options and accepting a slight rounding error, [tex]\( y = -1.74x + 36.2 \)[/tex] would be closest in terms of the slope, but it has an incorrect intercept.
Given the provided correct numerical findings, there is no perfect match within the provided choices.
