Linear Functions — Quiz

Question 3 • Algebraic Reasoning

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, 'negative 4'; Column 2, 'negative 5' Row 3: Column 1, 'negative 3'; Column 2, 'negative 4' Row 4: Column 1, 'negative 2'; Column 2, 'negative 2' Row 5: Column 1, '2'; Column 2, '2' Row 6: Column 1, '4'; Column 2, '5'

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

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

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

Explanation

A table represents a linear function when the rate of change in y per unit change in x stays constant. In choice B, each time x increases by 2, y increases by 2, and from x = −1 to 0 and from 0 to 2, the rate is also 1 per unit. Thus the points follow the linear rule y = x + 3. The other tables have changing rates of change.

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