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All courses Math Foundations · MF.PR.6 20 of 60
Find and interpret the constant of proportionality in multiple representations.

Find k from a table

Problem
Use the table to find the constant of proportionality.
A clear two-column table for a proportional relationship with headers x and y. The rows are 3 and 12, 5 and 20, and 7 and 28. Text above says to find k in the equation y = kx. Open full size
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Hint

Pick one complete row from the table, like x = 3 and y = 12, and find y divided by x.

In a proportional relationship written as y = kx, the constant of proportionality is the same y-to-x ratio in every row.

Solution walkthrough

01

Solve the proportional equation for k

\[y~=~kx,~\text{so}~k~=~y/x\]

Because y is the output and x is the input, the constant is output divided by input.

02

Use one table pair

\[k~=~12/3~=~4\]

The first stated row gives x = 3 and y = 12.

03

Check the other rows

\[20/5~=~4~\text{and}~28/7~=~4\]

Both remaining pairs give the same multiplier, confirming the table is proportional with k = 4.

04

State the constant

\[4\]

The constant of proportionality in y = kx is 4.

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Another way

  1. Notice that each y-value is four times its paired x-value: 12 = 4(3), 20 = 4(5), and 28 = 4(7).

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Common mistake

Do not reverse the division. The equation y = kx requires k = y/x, not x/y.

Solution walkthrough video