Uvero — STEM Learning

Finding a Linear Rule from a Table

A constant first difference in outputs for equal input steps signals a linear rule. The output change gives gradient; one row determines the intercept. A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Outputs rise by 2 for each input step, so $m=2$ .
At $x=0$ , $y=3$ , so $y=2x+3$ .

A table follows $(x,y)=(0,3),(1,5),(2,7)$ . Write the rule.

Which statement best captures the central mathematical idea in Finding a Linear Rule from a Table?

The output change gives gradient; one row determines the intercept.

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Finding a Linear Rule from a Table, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for finding a linear rule from a table.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Finding a Linear Rule from a Table?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

The output change gives gradient; one row determines the intercept.

Represent the given information clearly and identify the operation or relationship required for finding a linear rule from a table.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.