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Does each set of points have a linear relationship? Justify your answer.

a) (-6, -4), (-5, -2), (-4, 0), (-3, 2), (-2, 4), (-1, 6), (0, 8), (1, 10), (2, 12), (3, 14)

a) Yes
b) No

b) (0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25), (6, 36)

a) Yes
b) No

User Blobbie
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1 Answer

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Final answer:

Set a) has a linear relationship because each increase in x results in a consistent increase of 2 in y, suggesting a straight line with a positive slope. Set b) does not have a linear relationship because the differences between y-values increase as x increases, indicating a quadratic relationship.

Step-by-step explanation:

To determine whether each set of points has a linear relationship, we can look for common differences between x-values and y-values or calculate the slope between the points.

Set a)

The points provided are: (-6, -4), (-5, -2), (-4, 0), (-3, 2), (-2, 4), (-1, 6), (0, 8), (1, 10), (2, 12), (3, 14).

Observing the change in x and y values, we see that for every increment of 1 in x, y increases by 2. This constant change suggests a straight line with a positive slope. Hence, these points do exhibit a linear relationship.

Set b)

The points are: (0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25), (6, 36).

The difference between y-values is increasing as x increases - this is characteristic of a quadratic relationship, not a linear one. Therefore, these points do not have a linear relationship.

User Janick Bernet
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