N/A — Exam

Question 37 • Mathematics I

Which table represents a direct variation function?

Answer

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5 point 5'; Column 3, 'negative 4 point 5'; Column 4, 'negative 3 point 5'; Column 5, 'negative 2 point 5'; Column 6, 'negative 1 point 5' Row 2: Column 1, 'y'; Column 2, '10'; Column 3, '8'; Column 4, '6'; Column 5, '4'; Column 6, '2'

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5 point 5'; Column 3, 'negative 5 point 5'; Column 4, 'negative 5 point 5'; Column 5, 'negative 5 point 5'; Column 6, 'negative 5 point 5' Row 2: Column 1, 'y'; Column 2, 'negative 3'; Column 3, 'negative 1'; Column 4, '2'; Column 5, '5'; Column 6, '10'

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 3'; Column 3, 'negative 1'; Column 4, '2'; Column 5, '5'; Column 6, '10' Row 2: Column 1, 'y'; Column 2, 'negative 4 point 5'; Column 3, 'negative 3 point 0'; Column 4, 'negative 1 point 5'; Column 5, '0 point 0'; Column 6, '1 point 5'

Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 3'; Column 3, 'negative 1'; Column 4, '2'; Column 5, '5'; Column 6, '10' Row 2: Column 1, 'y'; Column 2, 'negative 7 point 5'; Column 3, 'negative 2 point 5'; Column 4, '5 point 0'; Column 5, '12 point 5'; Column 6, '25 point 0'

Explanation

A direct variation has the form y = kx, so the ratio y/x must be the same for every pair. In choice D, the ratios are (−7.5)/(−3) = 2.5, (−2.5)/(−1) = 2.5, and 25/10 = 2.5; the other pairs give the same ratio. Therefore, choice D, the table with y = 2.5x, represents a direct variation.

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