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
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GPT 3.5
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.
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.
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