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3.4 Two-Variable Data & Models - Scatterplots and correlation
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In which of the following tables is the relationship between the values of x and their corresponding y-values nonlinear?

A.

The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 8. Column 2. x is 2. y is 13. Column 3. x is 3. y is 18. Column 4. x is 4. y is 23.

B.

The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 6. Column 2. x is 2. y is 12. Column 3. x is 3. y is 24. Column 4. x is 4. y is 48.

C.

The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 8. Column 2. x is 2. y is 11. Column 3. x is 3. y is 14. Column 4. x is 4. y is 17.

D.

The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x,” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 4. Column 2. x is 2. y is 8. Column 3. x is 3. y is 12. Column 4. x is 4. y is 16.

In which of the following tables is the relationship between the values of x and their

Hard-difficulty · SAT Math · Two-Variable Data & Models — Scatterplots and correlation. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer 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.

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