Question

The table shows the relationship between two variables. Is the table linear? Nonlinear? Increasing? Decreasing? x: 1,2,3,4 y: 5,-1, -7, -13

Answer 1

To determine if the relationship between two variables is linear or nonlinear, we need to analyze the pattern of the data in the table.

Based on the given table:

x: 1, 2, 3, 4
y: 5, -1, -7, -13

Let's calculate the differences between successive values of x and y:

Δx: 1, 1, 1
Δy: -6, -6, -6

If the values of Δy are constant, it indicates a linear relationship. In this case, Δy is -6 for each Δx. Therefore, the relationship between the variables x and y is linear.

Additionally, we can identify whether the relationship is increasing or decreasing based on the values of y. In this case, as x increases, y decreases. Therefore, the relationship is decreasing.

In conclusion, the relationship between the variables x and y in the given table is linear and decreasing.