To determine the relationship between the number of music files and the storage space used, we can analyze the data provided in the table. Let's outline the steps to find this relationship:
1. Data Representation:
- The data points from the table are:
- (10 files, 15 MB)
- (20 files, 30 MB)
- (30 files, 45 MB)
- (40 files, 60 MB)
- (50 files, 75 MB)
2. Trend Analysis:
- Looking at this data, we can observe a pattern. As the number of files increases, the storage space used also increases. Specifically, there appears to be a consistent increment in both the number of files and the amount of storage space.
3. Linear Relationship:
- To confirm this observation, we can fit a linear model to the data. The linear model can be represented by the equation [tex]\( \text{space used} = \text{slope} \times \text{number of files} + \text{intercept} \)[/tex].
4. Calculate the Slope and Intercept:
- From calculations, we determine:
- Slope: [tex]\( 1.5 \)[/tex]
- Intercept: [tex]\( -7.680472963235736 \times 10^{-15} \approx 0 \)[/tex]
- The slope of 1.5 implies that for every additional music file, the storage space increases by 1.5 MB.
- The intercept is essentially zero, indicating that the linear relationship passes through the origin (0 files, 0 MB).
5. Final Statement:
- Based on the determined slope and intercept, we analyze the relationship:
- The positive slope shows that as the number of files increases, the storage space used increases.
Thus, the statement that best describes the relationship between storage space and the number of music files is:
As the number of files increases, the storage space used increases.
