# SAT Math Multiple Choice Question 260: Answer and Explanation

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**Question: 260**

**5.** Which of the following does not represent a linear relationship?

- A.
x -1 -4 -7 -10 -13 y 8 6 4 2 0 - B.
x -3 -1 1 3 5 y 5 3 1 -1 -3 - C.
x 1 2 3 4 5 y -5 -5 -5 -5 -5 - D.
x -2 -1 0 1 2 y 4 1 0 1 4

**Correct Answer:** D

**Explanation:**

D

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: Check to see whether the change in the y-values compared with the change in the x-values is constant for each pair of values.

Getting to the Answer: The table in (D) does not represent a linear relationship because the x-values change by +1 each time, while the y-values change by -3, then -1, then +1, then +3. A linear relationship has a constant rate of change, which means it is either always increasing or always decreasing by the same amount. This data clearly changes direction and is therefore not linear.