GOZUNTA
Try it now
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
The table shows a proportional relationship between x and y.

x | 3 | 5 | 7
y | 12 | 20 | 28

What is the constant of proportionality, k, in the equation y = kx?
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
Your answer
With a free account

Turn browsing into a plan.

Pick an objective, make a session, and give your practice a clear beginning and end.

Create a free account
With paid access

Follow a skill back to its prerequisites.

All-course access lets you move between Math Foundations and Math I–III when an earlier idea needs attention.

Compare plans

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

Pick one row from the table

\[(x,~y)~=~(3,~12)\]

In a proportional relationship, the constant of proportionality is the same in every row, so one complete row is enough to find k.

02

Use y divided by x

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

Because the equation is y = kx, k is the multiplier that turns x into y. That means k = y ÷ x, not x ÷ y.

03

Check another row

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

The ratio matches in the other rows, so the table is consistently proportional with the same constant.

04

State the constant of proportionality

\[k~=~4\]

The number that multiplies each x-value to get the y-value is 4.

+

Another way

  1. Start with 12 = 3k from the first row, then divide both sides by 3 to get k = 4.

!

Common mistake

A common mistake is computing 3/12 = 1/4. That reverses the ratio. Since the equation is y = kx, you must divide y by x, so use 12/3, not 3/12.