In this activity, you will use a table of coordinate points to determine whether a function is linear or nonlinear. Billy hit a baseball to the bottom of the outfield wall. The table gives points in the function representing the height of the baseball in terms of the horizontal distance traveled by the ball. Help Billy find whether this function is linear or nonlinear. x y
0 3
150 78
300 3
The value of x represents the horizontal distance traveled by the baseball, and the value of y represents the height of the ball from the ground.

Part A
To determine whether a function is linear or nonlinear, check whether the rate of change is constant for every pair of coordinates. What is the rate of change, change in y/change in x, for the first two pairs of coordinates?

Part B
Now, check the function’s rate of change over different pairs of coordinates. What is the rate of change, change in y/change in x, for the second and third pairs of coordinates?

Part C
Are the two rates of change the same? Explain your answer.

Part D
Depending on whether the rates are the same or different, you can infer whether the points could represent a linear function. Could the function be a linear function?