Question

The table shows the height of a softball that Hallie threw in the air. Is the relationship shown linear? Why or why not?

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I know it's not linear but I dont know why.​

Answer 1

Not a linear relationship

Explanation:

Given

The attached table

Required

Linear or not

To do this, we simply calculate the slope of the table at different intervals.

Slope (m) is calculated as:

`m = (y_2 - y_1)/(x_2 - x_1)`

Let:

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (0.5,7.2)`

So, the slope is:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (7.2 - 0)/(0.5-0)`

`m = (7.2)/(0.5)`

`m = 14.4`

Let:

Let:

`(x_1,y_1) = (1,10.7)`

`(x_2,y_2) = (2,12.2)`

So, the slope is:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (12.2 - 10.7)/(2 - 1)`

`m = (1.5)/(1)`

`m = 1.5\\`

See that the calculated slopes are not equal.

Hence, it is not linear