Question

Can someone help me please

Answer 1

Answer: Choice A) -3/2

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Step-by-step explanation:

Focus on the endpoints (0,15) and (10,0). They are the y and x intercepts in that order. This is the starting point and ending point of the ball.

The average rate of change is the slope of the line connecting these endpoints. This is when we consider the entire time the ball is in the air.

Let's use the slope formula to get the following:

`(x_1,y_1) = (0,15) \text{ and } (x_2,y_2) = (10,0)\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\m = (0 - 15)/(10 - 0)\\\\m = (-15)/(10)\\\\m = -(3)/(2)\\\\`

The slope is -3/2, which is the average rate of change.

It tells us that the height is decreasing by 3/2 = 1.5 meters per second, which is an average speed.

In other words, the ball is going downward at an average speed of 1.5 meters per second.

Keep in mind the instantaneous speed of the ball is changing all the time. The result of -3/2 = -1.5 only applies to the average speed.

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Note how the slope formula involves computing the change in y (which was us computing
`y_(2) - y_(1) = 0 - 15 = -15`. It indicates the ball had gone down 15 meters when going from the start point to the ending point. This is the change in distance. The change in time is the
`x_(2) - x_(1) = 10-0 = 10` portion, meaning the duration is 10 seconds.

In short,

slope = rise/run

slope = (change in distance)/(change in time)

slope = (-15)/(10)

slope = -3/2

So this may be a better way to see what's going on rather than rely on a formula in the previous section.