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Which Table Represents a Linear Function? Edgenuity Answer

The linear table is the one whose y-values increase by one-half whenever x increases by 1. That constant first difference gives slope 1/2 and the equation y = (1/2)x.

Question

Which table represents a linear function?

Table A

x1234
y1/211 1/22

Table B

x1234
y11/21/31/4

Table C

x1234
y791321

Table D

x1234
y061630

Answer

The first table represents a linear function.

xx1234
yy12\frac1211121\frac122

Each time xx increases by 1, yy increases by 12\frac12:

Δy=12,Δx=1,ΔyΔx=12.\Delta y=\frac12,\qquad \Delta x=1, \qquad \frac{\Delta y}{\Delta x}=\frac12.

The rate of change is constant, so the points lie on one straight line. The equation is

y=12x.y=\frac12x.

Check the other tables

Second table

The outputs are 1,12,13,141,\frac12,\frac13,\frac14. Their first differences are not constant. This table follows the reciprocal rule y=1xy=\frac1x, which is nonlinear.

Third table

The outputs are 7,9,13,217,9,13,21. Their consecutive differences are 2,4,82,4,8, so the rate of change changes. The table is nonlinear.

Fourth table

The outputs are 0,6,16,300,6,16,30. Their consecutive differences are 6,10,146,10,14, so this table is also nonlinear.

Fast method

When the xx-values increase by equal amounts, subtract consecutive yy-values. A linear table must have the same first difference throughout. If the xx-increments are unequal, compare Δy/Δx\Delta y/\Delta x for every interval instead.

Evidence boundary

This answer matches the publicly visible Edgenuity Introduction to Linear Functions quiz item whose four tables use x-values 1, 2, 3, and 4 and the listed y-values. Edgenuity may randomize table order or values between course versions, so identify the constant rate rather than relying on an option position alone.

Sources

These references support the concepts and methods used in the explanation above.

Which Table Represents a Linear Function? Edgenuity Answer | Verla