L3 · Tables of values from a linear relation

Learning goal

“I can build a table of values from a linear relation, spot the constant difference in the output column, and use the table to answer questions about the relation.”

Table of values — a chart pairing each input with its output, computed from a relation.

Input — the value you choose and substitute (often called x); it goes in the first row or column.

Output — the value the relation produces (often called y); it goes in the second row or column.

Constant difference — in a linear relation's table, the outputs grow by the same amount every time the input grows by 1. That amount is the number multiplying the input.

Worked example

Build a table for y = 2x + 3, for x = 0, 1, 2, 3, 4. Step 1: One row at a time, substitute: x = 0 -> y = 2(0) + 3 = 3. x = 1 -> 5. x = 2 -> 7. x = 3 -> 9. x = 4 -> 11. Step 2: Read the table back: inputs 0, 1, 2, 3, 4; outputs 3, 5, 7, 9, 11. Step 3: Check the constant difference: 5 - 3 = 2, 7 - 5 = 2, 9 - 7 = 2. The outputs climb by exactly 2 - the number multiplying x. If a row breaks the pattern, that row has an arithmetic error. The table checks itself. Say it plainly: a table turns one rule into many (input, output) pairs. Those pairs are exactly what we will plot as points in the next lesson.

Check yourself — explain it

In the table for y = 2x + 3, the outputs grow by 2 each row because...

Paired problem — example still visible

Build the table for y = 3x + 1 at x = 1, 2, 3. -> 4, 7, 10 (constant difference 3)

Faded completion — last step is yours

"y = 4x - 1: x = 2 gives 7; x = 3 gives ___" -> 11

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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