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MathidiaMathematics Academy
Linear graphs
Lesson 31 of 75
Introduction

Coordinates from rules

Objective. Generate coordinate pairs from linear rules.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Generating coordinate pairs from a rule means substituting chosen x-values into a linear equation to find matching y-values, producing a table ready for plotting. Choose a spread of x-values including negatives and zero, substitute each into the rule, and record the resulting pairs. For y = 2x − 1, substituting x = −1, 0, 1, 2 gives y = −3, −1, 1, 3, so the pairs are (−1, −3), (0, −1), (1, 1), (2, 3). Always substitute carefully, working through the order of operations each time.

Worked example

Complete the coordinate pair for the rule y = 3x + 2 when x = −2.

3 … 2
Coordinate grid with the line 3 … 2
  1. 1Substitute x = −2 into the rule: y = 3(−2) + 2
  2. 2Multiply first: 3 × (−2) = −6
  3. 3Add 2: −6 + 2 = −4
  4. 4The coordinate pair is (−2, −4)

Answer: (−2, −4)

Concept mastery

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Practice

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Common mistake. Pupils often substitute x into only part of the expression, computing y = 2x − 1 as 2(x − 1) and getting the wrong value. Always apply the rule exactly as written, multiplying before subtracting.

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