We are given a table that shows the heights in feet of a baseball x seconds after it was hit.
Seconds, x
Height (feet), y
0
3
0.5
39
1
67
1.5
87
2
99
Let's find an equation of a line of best fit to help us predict the height of the ball after 5 seconds. First, let's enter the data from the table into our calculator. Start by pressing the STAT button and selecting Edit. Enter the x-values in the first list and the y-values in the second.
Next we press STAT again, go to the CALC menu, and press 4, which corresponds to linear regression. Then we scroll down and select Calculate.
We can see that the slope of the line is 48 and its y-intercept is 11. Let's use this information to write the equation of the line of best fit in slope-intercept form.
y= 48x+ 11
Finally, let's substitute 5 into our equation for x and find the value of y. This value will represent the height of the baseball after 5 seconds.
We predict that the height of the baseball after 5 seconds will be 251 feet.
We are given that after 5 seconds, the actual height of the baseball is 3 feet, not the 251 feet that we predicted in Part A. To understand why our prediction was incorrect, let's think about the shape of the trajectory of the baseball after it is hit. Let's make a scatter plot with the given points, then extend it to show our estimated trajectory.
When we hit a baseball, it will be rise and then fall down. Due to gravity, there is no possibility that a ball will continue rising all the time. Therefore, the height of the ball is not linear. This is why our prediction is incorrect.
