Final answer:
The best-fit linear regression line for the given points is option B, y= -1.4x + 7.6, which has the appropriate negative slope and y-intercept close to the first data point.
Step-by-step explanation:
The question pertains to finding the linear regression line that best fits a given set of points. A linear regression line can be written in the form y = mx + b, where 'm' represents the slope of the line, and 'b' is the y-intercept. We can tell if an option is more likely to be the correct one by comparing the given points to the predicted y-values from each equation's slope and y-intercept.
To determine which equation from the options given best fits the data points (0,8), (1,6), (1,7), (2,4), (2,5), (4,1), (5,1), (6,0), we can analyze the slope and y-intercept of each option. The slope indicates how steep the line is, and the y-intercept is where the line crosses the y-axis (when x=0).
Comparing the options to the points, we notice two things:
- The y-intercept must be close to 8 since when x=0, y is 8.
- The slope must be negative since as x increases, y decreases.
Based on these observations, we can eliminate any options that do not have a negative slope or a y-intercept around 8. After inspecting every option and estimating the closeness of fit to the provided points, we determine that: Option B, y= -1.4x + 7.6, is the best fit for the data provided. It has a negative slope which aligns with the downward trend of the points, and a y-intercept close to the value of y when x is 0.