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Straight line graphs

Straight line graphs for ESOL Engineering: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Engineering
  • Spec R16 · R12 · R6
  • 12 min read
  • 7 revision boxes

Introduction

2 boxes
3 min read

What is straight line graphs?

Listen to this box

Transcript

A short spoken summary of straight line graphs and where it is used.

A spoken walk-through of straight line graphs before you read the notes.
Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ×10\times 10 moves every digit one column left.
3 rows

The straight line graphs reference table

Practise the routine version until it is automatic, then move to the multi-step questions.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
×10\times 10 moves every digit one column left
Row 2 column 4
Row 2 column 5

Learning

3 boxes
3 steps

How to work with straight line graphs

The examiner marks the working, so a correct answer with no method still drops marks.
The layout below is the one the mark scheme expects.

Diagram showing straight line graphs laid out step by step

The same idea drawn out, so the method is visible.
  1. Read the question and write down what is being asked for.
  2. Set out the working for straight line graphs in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Straight line graphs

This idea appears again in the higher-mark questions, so it is worth over-learning.

  • Rule 1

    How straight line graphs behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How straight line graphs behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How straight line graphs behaves in the 3rd of the cases the specification names.
    ≈160\approx 160
4 steps

How to work with straight line graphs

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
  1. Read the question and write down what is being asked for.
  2. Set out the working for straight line graphs in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: ≈160\approx 160

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Examples

2 boxes
1 marks · worked

Worked example: straight line graphs

Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing straight line graphs laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
2 marks · worked

Practice question 7: 34×25\frac{3}{4} \times \frac{2}{5}

Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing straight line graphs laid out step by step

The same idea drawn out, so the method is visible.

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Common questions

How many marks is straight line graphs usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the ESOL Engineering paper?
Yes — it sits in the Energy and matter strand.