Question
Hours Total Snow Accumulated (inches)
1 1.7
2 2.9
3 4.4
4 6.2
5 7.5
6 8.9
7 10.3
8 11.9
A weatherman collected data on snow accumulation. A line of best fit was computed. The equation for the line is: y=1.5+0.125. Which BEST interprets the slope of the linear model?
The snow is accumulating at 1.5 inches every hour
The snow is accumulating at 1 inch every 1.5 hours
The snow is accumulating at 1 inch every 0.125 hours
The snow is accumulating at 1.5 inches every 0.125 hours
1 1.7
2 2.9
3 4.4
4 6.2
5 7.5
6 8.9
7 10.3
8 11.9
A weatherman collected data on snow accumulation. A line of best fit was computed. The equation for the line is: y=1.5+0.125. Which BEST interprets the slope of the linear model?
The snow is accumulating at 1.5 inches every hour
The snow is accumulating at 1 inch every 1.5 hours
The snow is accumulating at 1 inch every 0.125 hours
The snow is accumulating at 1.5 inches every 0.125 hours
Answers
GPT-4o mini
To interpret the slope of the linear model represented by the equation \(y = 1.5 + 0.125x\), we need to understand what the slope (0.125) represents in the context of the data.
The slope of a linear equation in the form \(y = mx + b\) represents the change in the dependent variable (in this case, total snow accumulated in inches) for a one-unit increase in the independent variable (in this case, hours).
Here, the slope is \(0.125\), which means that for each additional hour, the total snow accumulated increases by \(0.125\) inches.
Now, let's analyze the provided options in the context of the slope:
1. **The snow is accumulating at 1.5 inches every hour.** (Incorrect - this doesn't relate to the slope of 0.125)
2. **The snow is accumulating at 1 inch every 1.5 hours.** (Incorrect - this is a re-interpretation, but it doesn't match the slope)
3. **The snow is accumulating at 1 inch every 0.125 hours.** (Incorrect - this implies a faster accumulation than 0.125)
4. **The snow is accumulating at 1.5 inches every 0.125 hours.** (Incorrect - this misrepresents the slope)
None of the options directly represent the correct understanding of the slope as 0.125 inches per hour. However, to express the accumulation accurately, we could say that:
- The snow is accumulating at 0.125 inches every hour.
Thus, the provided options do not include the correct interpretation of the slope as 0.125 inches per hour. Based on a more accurate view, if we were to convert the slope to another time frame, we would say that the snow accumulates approximately 1 inch every 8 hours (since \( \frac{1}{0.125} = 8\)). However, none of the answer choices accurately reflect this definitive interpretation.
The slope of a linear equation in the form \(y = mx + b\) represents the change in the dependent variable (in this case, total snow accumulated in inches) for a one-unit increase in the independent variable (in this case, hours).
Here, the slope is \(0.125\), which means that for each additional hour, the total snow accumulated increases by \(0.125\) inches.
Now, let's analyze the provided options in the context of the slope:
1. **The snow is accumulating at 1.5 inches every hour.** (Incorrect - this doesn't relate to the slope of 0.125)
2. **The snow is accumulating at 1 inch every 1.5 hours.** (Incorrect - this is a re-interpretation, but it doesn't match the slope)
3. **The snow is accumulating at 1 inch every 0.125 hours.** (Incorrect - this implies a faster accumulation than 0.125)
4. **The snow is accumulating at 1.5 inches every 0.125 hours.** (Incorrect - this misrepresents the slope)
None of the options directly represent the correct understanding of the slope as 0.125 inches per hour. However, to express the accumulation accurately, we could say that:
- The snow is accumulating at 0.125 inches every hour.
Thus, the provided options do not include the correct interpretation of the slope as 0.125 inches per hour. Based on a more accurate view, if we were to convert the slope to another time frame, we would say that the snow accumulates approximately 1 inch every 8 hours (since \( \frac{1}{0.125} = 8\)). However, none of the answer choices accurately reflect this definitive interpretation.