Which table represents a proportional function (M) x -1 1 3 4 y 0 0 16 30 x -1 1 3 4 y 0 0 16 30 (N) x -3 0 1 4 y -10 -4 -2 4 x -3 0 1 4 y -10 -4 -2 4 (O) x -15 -12 -6 3 y -5 -4 -2 1 x -15 -12 -6 3 y -5 -4 -2 1 (P) x -4 -2 -1 -2 y 9 7 5 9 x -4 -2 -1 -2 y 9 7 5 9

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Which table represents a proportional function (M) x -1 1 3 4 y 0 0 16 30 x -1 1 3 4 y 0 0 16 30 (N) x -3 0 1 4 y -10 -4 -2 4 x -3 0 1 4 y -10 -4 -2 4 (O) x -15 -12 -6 3 y -5 -4 -2 1 x -15 -12 -6 3 y -5 -4 -2 1 (P) x -4 -2 -1 -2 y 9 7 5 9 x -4 -2 -1 -2 y 9 7 5 9

Answer 1

# Explanation: ## Step 1: A proportional function is a function that always multiplies its input variable by a definite constant. This means that the ratio of the y-values to the x-values should be constant for all pairs of values. ## Step 2: Let's analyze each option: ### Option M: The x-values decrease by 2 each time — from -1 to 1, from 1 to 3, and so forth. However, the y-values do not change by the same multiple — from 0 to 0 and from 0 to 16. ### Option N: The x-values increase by 1 each time — from -3 to 0, from 0 to 1, and so forth. The y-values reduce by multiples of 2 each time — from -10 to -4, from -4 to -2, and from -2 to 4. Therefore, option (N) is a proportional function. ### Option O: The change in x-values decreases by 3 each time, and the y-values are not uniformly changed, so this option does not apply. ### Option P: We can notice a similar situation as above with the y-values. For the X, there is inconsistency from -1 to -2. Therefore, the table in option (P) does not represent a proportional function. # Answer: The table that represents a proportional function is option (N).

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Which table represents a proportional function (M) x -1 1 3 4 y 0 0 16 30 x -1 1 3 4 y 0 0 16 30 (N) x -3 0 1 4 y -10 -4 -2 4 x -3 0 1 4 y -10 -4 -2 4 (O) x -15 -12 -6 3 y -5 -4 -2 1 x -15 -12 -6 3 y -5 -4 -2 1 (P) x -4 -2 -1 -2 y 9 7 5 9 x -4 -2 -1 -2 y 9 7 5 9

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