Good Learning Co.
SavannahYear 8
← Maths
MathsAlgebraic reasoning30 min★★★ difficulty

Straight-line graphs in four quadrants

A straight-line graph is a picture of a rule. Once you can read gradient and intercept off the line, y = mx + c stops being something to memorise.

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

  • • All four quadrants
  • • Building a table of values
  • • Gradient and intercept
  • • Comparing and using lines

This lesson at a glance

  • 30 minutes
  • 19 parts to scroll through
  • 4 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 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Straight-line graphs in four quadrants

An English teaching video on this topic from CAST. 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

What you already know

Part 2 of 19

Before we start

What you already know

You can plot coordinates and substitute into expressions.

Recap: Solving equations that need rearranging
3

Key words

Part 3 of 19

Key words

Words you'll need today

gradient
How steep a line is: change in y divided by change in x.
y-intercept
Where the line crosses the y-axis.
quadrant
One of the four regions of the coordinate grid.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Part 1 — Plotting and reading

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

5

Explore the idea

Part 5 of 19

Learn

All four quadrants

Coordinates are always (x, y): across first, then up or down. In the third quadrant both are negative, such as (−3, −2). A common slip is reading (−3, 2) as three up and two left. Say 'along the corridor, up the stairs' every time and the order stays right.

6

Explore the idea

Part 6 of 19

Learn

Building a table of values

For y = 2x − 1, choose x values including negatives: x = −2, −1, 0, 1, 2 gives y = −5, −3, −1, 1, 3. Plot and join with a ruler. If one point is out of line, that y value is wrong — a straight-line rule cannot produce a kink.

7

Quick check

Part 7 of 19

Quick check

Which point is in the third quadrant?

8

Quick check

Part 8 of 19

Quick check

For y = 2x − 1, what is y when x = −3?

9

Reset break

Part 9 of 19

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
10

Learning cycle

Part 10 of 19

Learning cycle 2 of 2

Part 2 — y = mx + c

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

11

Explore the idea

Part 11 of 19

Learn

Gradient and intercept

In y = mx + c, m is the gradient and c is the y-intercept. For y = 3x + 2 the line rises 3 for every 1 across and crosses the y-axis at 2. A negative gradient falls as you go right. From a graph, find the gradient by picking two clear points and dividing the rise by the run.

12

Explore the idea

Part 12 of 19

Learn

Comparing and using lines

Parallel lines share the same gradient. Steeper means a larger gradient, whatever the sign. Real graphs work the same way: on a distance-time graph the gradient is speed, so a steeper section means faster travel. Reading gradient as a rate is the idea GCSE keeps returning to.

13

Quick check

Part 13 of 19

Quick check

Gradient of y = 5 − 2x?

14

Quick check

Part 14 of 19

Quick check

Where does y = 3x − 4 cross the y-axis?

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Reading coordinates as (y, x).
  • Thinking c is the gradient in y = mx + c.
  • Calling a line with gradient −4 'less steep' than one with gradient 2.
16

Challenge round

Part 16 of 19

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

17

Challenge round

Part 17 of 19

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

____ are always (x, y): across first, then up or down.

Real ____ work the same way: on a distance-time graph the gradient is speed, so a steeper section means faster travel.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Straight-line graphs in four quadrants

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

  1. 1. y = mx + c: what is m?

  2. 2. Which line is parallel to y = 4x + 1?

  3. 3. A line falls as x increases. Its gradient is...

  4. 4. For y = −x + 6, y when x = 2?

  5. 5. On a distance-time graph, gradient shows...

  6. 6. Point (0, −5) lies...

19

Lesson round-up

Part 19 of 19

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?

Ask Luna

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 19 · Watch & discover

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