Question

what is the rate of change for the linear relationship modeled in the table? x y −1 10 1 9 3 8 5 7 -1/2 0 1/2 2

Answer 1

(-1,10)(1,9)
slope = (9 - 10) / (1 - (-1)
slope = -1/2 <=== slope is also ur rate of change

Answer 2

Rate of change for the linear relationship modeled is
`(-1)/(2)`

Explanation:

As the there is a linear relationship in the points, so all these points will be on a single straight line. Hence the slope will be same throughout all the points.

We know that, the slope of the line joining (x₁, y₁) and (x₂, y₂) is,

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

Putting the points as (-1, 10) and (1, 9), we get

`m=(9-10)/(1-(-1))`

`=(9-10)/(1+1)`

`=(-1)/(2)`

Rate of change is the slope of the line joining all these points.