Question

What is the rate of change for the linear relationship modeled in the table? (4 points)

x y

-1 10

1 9

3 8

5 7

negative one over two
0
one over two
2

Answer 1

Answer:1/2

Explanation:

Because the other guy said so and they seem smart so...yeah I would pick that one.

Answer 2

-1/2

Explanation:

In a linear relationship, the rate of change of one variable with respect to the other is constant. When we talk about change, we're looking for a difference of values.

If we look at the first and second rows, the change in x is 1 - (-1) = 2, while the change in y is 9 - 10 = -1. Usually we refer to these changes as Δx and Δy (read like "delta-x" and "delta-y"), and the rate of change is the number we get by dividing one of these by the other.

The rate of change we're used to seeing, sometimes called the slope, is Δy/Δx. So, using the values we've already found:

`\Delta{x}=2\\\Delta{y}=-1\\\Delta{y}/\Delta{x}=-1/2`