Learn how to find the constant of proportionality from any table of pairs. See every y ÷ x quotient, the value of k, the equation y = kx, and the matching graph.
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In grade 6 the same ratio is shown on a double number line — use the ratio table and double number line generator for that visual.
The Constant of Proportionality Calculator shows how to find the constant of proportionality from any set of (x, y) pairs. Enter your data and it builds the proportional relationship table with an explicit y ÷ x column, so you can see at a glance whether every quotient is the same.
Alongside the table it plots the pairs on a coordinate grid together with the origin. When the relationship is proportional the points lie on one straight line through (0, 0) and the tool reports k and the equation y = kx; when it is not, the line visibly bends and the tool names the row that broke the pattern. Built for Common Core 7.RP.A.2.
Divide y by x for every pair in the table. If every quotient is the same number, that number is the constant of proportionality k, and the relationship can be written as y = kx.
Check that the plotted points lie on one straight line that passes through the origin (0, 0). Then read the y-value of the point where x = 1: that y-value is k.
A relationship is proportional when every y ÷ x quotient is equal and the graph is a straight line through the origin. If one quotient differs, or the line does not pass through (0, 0), the relationship is not proportional.
It is the unit rate: the amount y changes for every 1 unit of x. If k = 3 miles per hour, then travelling 1 more hour always adds 3 more miles.
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