Table of Values

A table of values is a simple two-column list that pairs input values (x) with their matching output values (y) for an equation. It is the bridge between an equation and its graph: pick a few x-values, work out each y, and you have a set of points you can plot. Tables of values are especially handy for graphing linear equations.

1. Choose a few x-values — small numbers like −1, 0, 1, and 2 are easiest.
2. Substitute each x into the equation and calculate y.
3. Write each (x, y) pair as a row in the table.

For y = 2x + 1, substituting x = 0 gives y = 1; x = 1 gives y = 3; x = 2 gives y = 5. Those pairs become the rows of the table.

Each row of the table is a coordinate point. Plot the points on a grid and, for a linear relation, join them with a straight line. Because two points already fix a line, a table with three or four rows also gives you a built-in check: if one point is off the line, recheck that row. Reading points back the other way is covered in reading linear relation graphs.

In a linear relation the y-values change by the same amount each time x increases by one — a constant step. For y = 2x + 1 the y-values rise by 2 each row, which is the slope. Noticing this steady change is the key idea behind patterns in linear relations.

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• Algebra