Question

The table shows the relationship between two variables which selection describes the relationship

Answer 1

C. Decreasing; Linear.

Explanation:

We have been given a table that shows the relationship between two variables.

Let us find slope of our given values using slope formula.

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

Let us find rate of change for points (1,5) and (2,-1)

`m=(-1-5)/(2-1)`

`m=(-6)/(1)=-6`

Let us find slope for points (3,-7) and (4,-13).

`m=(-13--7)/(4-3)`

`m=(-13+7)/(1)`

`m=(-6)/(1)=-6`

We can see that rate of change is constant (-6), therefore, our function is a linear function. Since slope is negative (-6) and with each increase in x, our y is decreasing, therefore, our function is decreasing.