Question

this scatterplot shows a comparison of the number of gallons of gas used and the number of miles traveled by a variety of vehicles. the line of best fit for these data is also shown. which of the following changes to the data set would cause the slope of the line of best fit to decrease? select all that apply. data points are collected from several fuel - efficient cars and added to the scatterplot. data points are collected from several vehicles that average 10 miles to the gallon and added to the scatterplot. the points (1,30), (3,50), and (5,100) are removed from the scatterplot. the points (5,50), (3,35), and (1,15) are added to the scatterplot.

Explanation:

Step1: Analyze the effect of adding fuel - efficient cars

Fuel - efficient cars would have a higher distance per gallon. If we add data points from several fuel - efficient cars (which means for a given amount of gas used (x - value), the distance traveled (y - value) is higher than the current trend), this would make the line of best fit steeper (increase the slope).

Step2: Analyze the effect of adding 10 - miles - per - gallon vehicles

If vehicles average 10 miles to the gallon, for \(x\) gallons of gas used, the distance \(y = 10x\). Compared to the current line of best fit (which seems to have a higher slope, say if we assume a rough estimate from the scatter - plot, for example, if for \(x = 2\) gallons, the current line might give \(y\approx30\) (slope \(m=\frac{30}{2}=15\) in this rough estimate), adding \(y = 10x\) (slope \(m = 10\)) data points will pull the line of best fit down, decreasing the slope.

Step3: Analyze the effect of removing high - slope points

The points \((1,30)\), \((3,50)\), and \((5,100)\): The slope between \((1,30)\) and \((3,50)\) is \(m_1=\frac{50 - 30}{3 - 1}=\frac{20}{2}=10\), and between \((3,50)\) and \((5,100)\) is \(m_2=\frac{100 - 50}{5 - 3}=\frac{50}{2}=25\). Removing these relatively high - value (compared to the overall trend) points will decrease the slope of the line of best fit.

Step4: Analyze the effect of adding low - slope points

The points \((5,50)\) (slope \(m=\frac{50}{5} = 10\)), \((3,35)\) (slope \(m=\frac{35}{3}\approx11.67\)), and \((1,15)\) (slope \(m = 15\)). If the original line of best fit has a higher slope (from the visual of the scatter - plot), adding these lower - slope - relative points will decrease the slope of the line of best fit.

Answer:

Data points are collected from several vehicles that average 10 miles to the gallon and added to the scatterplot; The points \((1,30)\), \((3,50)\), and \((5,100)\) are removed from the scatterplot; The points \((5,50)\), \((3,35)\), and \((1,15)\) are added to the scatterplot.