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Using tables of values to graph proportional relationships

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Table of Values

A table of values pairs x-inputs with their matching y-outputs so you can plot an equation and draw its graph. Learn how to make one by substituting x-values into the equation, how to turn the rows into points on a graph, and how the constant step in the y-values reveals a linear pattern.

What a table of values is

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.

Table of values for y = 2x + 1 and its graph A table lists x values negative one, zero, one, two and the matching y values negative one, one, three, five for the equation y equals 2x plus 1. The four points are plotted on a coordinate grid and joined by a straight line. xy −1−1 01 13 25 xy y = 2x + 1
A table of values for y = 2x + 1 and the straight line through its points.

How to make a table of values

  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.

From table to graph

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.

Spotting a linear pattern

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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