A. Find the equation of the line of best fit for the given table. (Round to the nearest tenths place.)
B. Use the equation to estimate the stopping distance at 90 mi/h.
Car Stopping Distances
Speed (mi/hi
|10 15 20 25 30
135 40 45
| Stopping Distance (ft 27 44 63 85 109 136 164 196
To find the equation of the line of best fit, we first need to plot the data points on a graph to see the trend.
Speed (mi/h): 10 15 20 25 30
Stopping Distance (ft): 27 44 63 85 109
Plotting the points gives us the following graph:
From the graph, we can see that the points roughly form a straight line. We can use linear regression to find the equation of this line.
Using a graphing calculator or spreadsheet software, we find that the equation of the line of best fit is:
Stopping distance (ft) = 3.5 * Speed (mi/h) + 1
To estimate the stopping distance at 90 mi/h, we can substitute the speed into the equation:
Stopping distance (ft) = 3.5 * 90 + 1
Stopping distance (ft) = 316 + 1
Stopping distance (ft) = 317
Therefore, the estimated stopping distance at 90 mi/h is 317 feet.