Example Question - line of best fit
Here are examples of questions we've helped users solve.
Finding the Best-Fitting Equation for Scatterplot Data
To find the equation that best fits the data on a scatterplot, we look for the line that closely follows the trend of the data points. From what I can see in the image: 1. The slope of the line should be positive, as the points seem to increase as we move from left to right. 2. The y-intercept is the point where the line crosses the y-axis. At x = 0, the line should cross the y-axis around the value of 9. This information helps us eliminate some of the options: - Option A (\(y = \frac{1}{2}x + 9\)) has a positive slope and the correct y-intercept. - Option B (\(y = 2x + 9\)) also has a positive slope and the correct y-intercept. - Option C (\(y = \frac{1}{2}x - 9\)) has the correct slope direction but the incorrect y-intercept. - Option D (\(y = 2x + 9\)) is the same as option B, which appears to be an error in the image as it's duplicated and does not provide another distinct option. Now, to distinguish between the remaining options A and B (or D, since it's the same), we need to consider the steepness of the line in the scatterplot. Option A has a gentler slope (\(\frac{1}{2}\)) than Option B (2). By inspecting the graph, it looks like the data points rise slower than a slope of 2 for every increase in x (since a line with slope 2 would rise too steeply for these data points), which suggests that Option A with a slope of \(\frac{1}{2}\) and a y-intercept at 9 would be the best fit for the data. Thus, Option A, \(y = \frac{1}{2}x + 9\), is most likely the equation that best fits the data on the scatterplot.
Determining Line of Best Fit for Scatter Plot Data
The question asks which equation could represent the line of best fit for the data in the scatter plot. Since I cannot see the exact distribution of points on the scatter plot, I can’t give you a precise answer. However, I can guide you on how to determine which equation could be the best fit. You would look for the trend that the data points seem to follow and then match that trend with one of the given options: - A linear line that has a positive slope would mean as the number of trips to the library increases, the trips to the bookstore also increase. - A linear line with a negative slope would imply that as the number of trips to the library increases, the trips to the bookstore decrease. - A steeper slope would indicate a stronger relationship between the two variables. - The y-intercept is where the line crosses the y-axis (when x=0). Looking at the options provided: A. y = 1/2x + 5.5 - This line has a positive slope and a y-intercept of 5.5. B. y = x + 8 - This line also has a positive slope, but with a steeper slope than option A and a higher y-intercept of 8. C. y = x + 5 - This also suggests a positive relationship with the same slope as option B but a lower y-intercept. D. y = -2/3x + 6 2/3 - This is the only option with a negative slope, suggesting an inverse relationship. You would pick the equation that best approximates the central tendency of your data points. If your scatter plot shows a positive trend, then you would pick between options A, B, or C, depending on the steepness of the slope and where the line would likely cross the y-axis. If the trend is negative, then option D would be the correct choice. Please check your scatter plot and compare the trend with the given options to make the appropriate selection.
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