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All courses Math Foundations · MF.PR.5 19 of 60
Determine whether a relationship is proportional from a table, graph, equation, or context.

Check proportionality from a table

Problem
Use the table to decide whether the relationship between cups of rice and total cost is proportional.
Two-column table labeled Cups of rice and Total cost in dollars. The rows are 1 and 2.50, 2 and 5.00, 4 and 10.00, and 6 and 15.00. Open full size
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Hint

Start by finding the cost per cup in each row: divide total cost by cups of rice, using the same ratio each time.

A table is proportional only if every row has the same unit rate here, the same cost for 1 cup. Don’t focus on how much the cost increases from row to row.

Solution walkthrough

01

Read the table pairs

\[(\text{cups},\text{cost})~=~(1,\$2.50),~(2,\$5.00),~(4,\$10.00),~(6,\$15.00)\]

The inspected table lists four rice quantities with their total costs.

02

Calculate cost per cup in every row

\[\$2.50/1~=~\$5.00/2~=~\$10.00/4~=~\$15.00/6~=~\$2.50~\text{per}~\text{cup}\]

Every nonzero row has the same y-to-x ratio.

03

Write the common rule

\[\text{total}~\text{cost}~=~\$2.50~\times~\text{cups}\]

A single constant multiplier relates cups to cost, with no fixed starting amount.

04

Classify and cite the evidence

\[\text{Proportional},~\text{because}~\text{each}~\text{row}~\text{has}~\text{the}~\text{same}~\text{cost}~\text{per}~\text{cup}:~\$2.50.\]

The constant unit rate proves the table represents a proportional relationship.

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Another way

  1. Check that every row satisfies y = 2.50x.

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Common mistake

Do not require equal additive jumps between consecutive rows. The cup inputs do not increase by equal amounts; proportionality is tested with a constant ratio.

Solution walkthrough video