Answer :
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.
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.
