5
QuizMultiple Choice

Drawing Trend Lines

Question 5 • Pre-Algebra B

Joseph claims that a scatterplot in which the y-values increase as the x-values increase must have a linear association. Amy claims that the scatterplot could have a nonlinear association. Which statement about their claims is true?

Answer
A
Joseph is correct because only a line will increase along the whole data set. The scatterplot will have a positive, linear association.
B
Joseph is correct because only a line will decrease along the whole data set. The scatterplot will have a negative, linear association.
C
Amy is correct because a nonlinear association could increase along the whole data set, while being steeper in some parts than others. The scatterplot could be linear or nonlinear.
D
Amy is correct because only a nonlinear association could increase along the whole data set. A line has the same slope at any point, but a curve can get steeper at different points.

Explanation

When y-values increase as x-values increase, the association is positive, but that does not mean it must be linear. A straight line could show this pattern, or a curve could increase while becoming steeper or less steep in different regions. Therefore, Amy is correct that the scatterplot could be linear or nonlinear. Choice D is too strong because a line can also increase throughout.

AI-written and checked against the verified answer.

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