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SavannahYear 8
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MathsNumber, algebra and geometry: connected foundations32 min★★ difficulty

Chapter 6: Coordinates and straight-line graphs

A straight-line graph turns an algebraic rule into a picture whose gradient and intercept carry meaning.

Part of your national curriculum
  • Algebra: Work with coordinates in all four quadrants and recognise, sketch and produce graphs of linear functions

Lesson overview

What you'll learn in this lesson

Work with coordinates in all four quadrants and recognise, sketch and produce graphs of linear functions

Key learning points

  • • Coordinates
  • • Generate a line
  • • Read the structure

This lesson at a glance

  • 32 minutes
  • 14 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

coordinatesquadrantssketchgraphslinear

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Chapter 6: Coordinates and straight-line graphs

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Work with coordinates in all four quadrants and recognise, sketch and produce graphs of linear functions

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · Coordinates

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 14

Learn

Coordinates

Coordinates are written (x,y): move horizontally first, then vertically. Negative coordinates locate points left of or below the origin.

4

Explore the idea

Part 4 of 14

Learn

Generate a line

For y = 2x + 1, choose x-values, calculate y, plot the points and join them with a straight line. Points include (0,1), (1,3) and (2,5).

5

Quick check

Part 5 of 14

Quick check

Which point lies in quadrant III?

6

Reset break

Part 6 of 14

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 14

Quick check

For y=2x+1, find y when x=3.

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Read the structure

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 14

Learn

Read the structure

In y = mx + c, m is the gradient and c is the y-intercept. Parallel lines have equal gradients.

10

Quick check

Part 10 of 14

Quick check

What is the gradient of y=−3x+4?

11

Challenge round

Part 11 of 14

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

____ are written (x,y): move horizontally first, then vertically.

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Chapter 6: Coordinates and straight-line graphs

3 questions, marked with the reasoning shown. No timer.

  1. 1. Which point lies in quadrant III?

  2. 2. For y=2x+1, find y when x=3.

  3. 3. What is the gradient of y=−3x+4?

14

Lesson round-up

Part 14 of 14

Lesson round-up

Ready when you are

Quiz score

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Games

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Points this lesson

0

Best run

0 in a row

Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

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Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 14 · Watch & discover

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    Work with coordinates in all four quadrants and recognise, sketch and produce graphs of linear functions

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