What you’ll learn
Identify proportional relationships from tables.
Key idea
If all quotients are equal, one constant k works in y = kx. If the quotients differ, the relationship is not proportional. A row with input zero should have output zero for a proportional relationship.
Use a consistent orientation: output divided by input. A table may increase in a regular pattern without being proportional, so equal increments alone are not enough. Once the ratio is confirmed, state k and attach the context's units.
Worked example
Classify examples and non-examples for the concept 'Identify proportional relationships from tables'.
Table x:(0, 5, 6, 7), y:(3, 13, 15, 17). Classify its proportionality using all nonzero ratios and the zero row.
- The zero row is (0,3); nonzero outputs follow y=2x+3.
- Ratios differ because a positive fixed output is divided by changing inputs; the table is not proportional.
Answer: Non-example — a nonzero zero-row output and differing ratios violate y=kx.
Quick Check
Classify examples and non-examples for the concept 'Identify proportional relationships from tables'.
Table x:(0, 2, 3, 4), y:(0, 8, 12, 16). Classify its proportionality using all nonzero ratios and the zero row.