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Problem-Solving and Data Analysis Difficulty: Medium

In which of the following tables is the relationship between the values of x and their corresponding y-values nonlinear?

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Explanation

Choice D is correct. The relationship between the values of x and their corresponding y-values is nonlinear if the rate of change between these pairs of values isn’t constant. The table for choice D gives four pairs of values: $the point with coordinates 1 comma 6$ , $the point with coordinates 2 comma 12$ , $the point with coordinates 3 comma 24$ , and $the point with coordinates 4 comma 48$ . Finding the rate of change, or slope, between $the point with coordinates 1 comma 6$ and $the point with coordinates 2 comma 12$ by using the slope formula, $the fraction with numerator y sub 2 minus y sub 1, and denominator x sub 2 minus x sub 1, end fraction$ , yields $the fraction with numerator 12 minus 6, and denominator 2 minus 1, end fraction$ , or 6. Finding the rate of change between $the point with coordinates 2 comma 12$ and $the point with coordinates 3 comma 24$ yields $the fraction with numerator 24 minus 12, and denominator 3 minus 2, end fraction$ , or 12. Finding the rate of change between $the point with coordinates 3 comma 24$ and $the point with coordinates 4 comma 48$ yields $the fraction with numerator 48 minus 24, and denominator 4 minus 3, end fraction$ , or 24. Since the rate of change isn’t constant for these pairs of values, this table shows a nonlinear relationship.

Choices A, B, and C are incorrect. The rate of change between the values of x and their corresponding y-values in each of these tables is constant, being 3, 4, and 5, respectively. Therefore, each of these tables shows a linear relationship.