Question

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

Answer 1

Answer:

Not a linear relationship

Step-by-step 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:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let:

$(x_1,y_1) = (0,0)$

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

So, the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{7.2 - 0}{0.5-0}$

$m = \frac{7.2}{0.5}$

$m = 14.4$

Let:

Let:

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

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

So, the slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{12.2 - 10.7}{2 - 1}$

$m = \frac{1.5}{1}$

$m = 1.5$

See that the calculated slopes are not equal.

Hence, it is not linear