Alright, let's analyze the given equation of the line of best fit:
[tex]\[ y = 92.73x + 31.82 \][/tex]
The general form of the equation of a line is:
[tex]\[ y = mx + b \][/tex]
where \( m \) is the slope and \( b \) is the y-intercept. Here's how we can interpret this in the context of the problem:
1. Slope (`m`): In this equation, the slope (\( m \)) is 92.73. The slope represents the rate of change of \( y \) with respect to \( x \). Given the context, \( x \) represents the number of months, and \( y \) represents the amount of money saved. Therefore, the slope of 92.73 indicates that Hannah saves $92.73 each month.
2. Y-intercept (`b`): The y-intercept (\( b \)) is 31.82. The y-intercept represents the value of \( y \) when \( x \) is 0. In this context, when the number of months (\( x \)) is 0, the amount \( y \) represents the initial amount of money in Hannah's trip account, which is $31.82.
Let's match this interpretation with the given statements:
- Statement A: "The [tex]$y$[/tex]-intercept of the line is 92.73, meaning that Hannah needed $92.73 to go on her trip."
- Incorrect. The y-intercept is 31.82, not 92.73.
- Statement B: "The slope of the line is 92.73, meaning that on average, Hannah saved $92.73 each month."
- Correct. This statement correctly identifies the slope and its interpretation.
- Statement C: "The slope of the line is 31.82, meaning that Hannah initially put $31.82 into her trip account."
- Incorrect. The slope is 92.73, not 31.82. 31.82 is the y-intercept.
- Statement D: "The [tex]$y$[/tex]-intercept of the line is 31.82, meaning that on average, Hannah saved $31.82 each month."
- Incorrect. The y-intercept is indeed 31.82, but it represents the initial amount in the trip account, not the average monthly saving.
Considering the analysis above, the correct statement is:
- B. The slope of the line is 92.73, meaning that on average, Hannah saved $92.73 each month.
So the correct choice is 2 (B).
