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Question 20 • Algebra II

Which table shows a linear function?

Answer

Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '0'; Column 2, 'negative 2' Row 3: Column 1, '1'; Column 2, '0' Row 4: Column 1, '2'; Column 2, '2' Row 5: Column 1, '3'; Column 2, '7' Row 6: Column 1, '4'; Column 2, '14'

Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 6'; Column 2, 'negative 16' Row 3: Column 1, 'negative 2'; Column 2, 'negative 8' Row 4: Column 1, '0'; Column 2, 'negative 4' Row 5: Column 1, '1'; Column 2, 'negative 2' Row 6: Column 1, '3'; Column 2, '2'

Table with 2 columns and 6 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, 'negative 2'; Column 2, 'negative 7' Row 3: Column 1, 'negative 1'; Column 2, '0' Row 4: Column 1, '0'; Column 2, '1' Row 5: Column 1, '1'; Column 2, '2' Row 6: Column 1, '2'; Column 2, '9'

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

Explanation

A table represents a linear function when the rate of change in y per change in x is constant. In choice B, each pair of consecutive points has slope 2: for example, from x = -6 to x = -2, y increases by 8 while x increases by 4, giving 8 ÷ 4 = 2. The other intervals also have slope 2, so choice B, the table with a constant rate of change, shows a linear function.

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