To find the equation of the line of best fit, we estimate the slope and y-intercept from the scatter plot. With this information, we can write the equation. To predict the time spent exercising for a given time spent texting, we substitute the x-value into the equation.
To approximate the equation of the line of best fit, we need to find the slope and the y-intercept. We can do this by using the data points on the scatter plot. From the graph, it appears that the line has a positive slope, meaning that as the time spent texting increases, the time spent exercising also increases. We can estimate the slope by picking two points on the line and finding the difference in the y-coordinates divided by the difference in the x-coordinates. Let's say we choose the points (0, 7) and (10, 0). The difference in the y-coordinates is 7 - 0 = 7, and the difference in the x-coordinates is 10 - 0 = 10. So the estimated slope is 7/10, which simplifies to 0.7.
Next, we need to find the y-intercept by extending the line so it crosses the y-axis. From the scatter plot, it looks like the line crosses the y-axis at y = 12. Therefore, the estimated y-intercept is 12.
Combining the estimated slope and y-intercept, we can write the approximate equation of the line of best fit as y = 0.7x + 12.
To predict the time spent exercising for a student who spends 6 hours texting, we substitute x = 6 into the equation. By plugging in x = 6, we get y = 0.7 * 6 + 12 = 4.2 + 12 = 16.2. Therefore, we predict that a student who spends 6 hours texting will spend approximately 16.2 hours exercising.
The probable question may be:
H Approximating the equation of a line of best fit and making predictions The scatter plot shows the time spent texting, x, and the time spent exercising, y, by each of 24 students last week. (a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit. (b) Using your equation from part (a), predict the time spent exercising for a student who spends 6 hours texting. Note that you can use the graphing tools to help you approximate the line. Time spent exercising (in hours) Explanation 10- Type here to search 0- sx 7- x Check Time spent texting (in hours) O H X EO Ś (a) Write an approximate equation of the line of best fit. y = (b) Using your equation from part (a), predict the time spent exercising for a student who spends 6 hours texting