Real-life graphs.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Real-life graphs

Graphs

Lesson 4 of 8

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before

Graphs

Lesson 4 of 8

Answer each one, then check.

1

Last lesson: what does the gradient of a distance-time graph show?

2

What is the y-intercept of y = 1.5x + 3?

3

5 miles is about 8 km. About how many km is 20 miles?

4

Work out 20 + 0.05 × 300.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Last Lesson and Before - Answers

Graphs

Lesson 4 of 8

1

Last lesson: what does the gradient of a distance-time graph show?

Speed

2

What is the y-intercept of y = 1.5x + 3?

3

3

5 miles is about 8 km. About how many km is 20 miles?

32 km

4

Work out 20 + 0.05 × 300.

35

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Graphs

Lesson 4 of 8

1

Use conversion graphs.

2

Draw and read cost graphs, and explain the gradient and intercept.

3

Use graphs to compare two options.

4

Match container shapes to graphs of depth against time.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

A Conversion Graph

Graphs

Lesson 4 of 8

25 miles is about 40 km.

A conversion graph is a straight line through the origin, because the two units are in direct proportion. Read up from one axis to the line, then across to the other. For values off the graph, scale up: 125 miles is 5 × 25 miles, so about 5 × 40 = 200 km.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Cost Graphs

Graphs

Lesson 4 of 8

A taxi charges a fixed £3, plus £1.50 per mile: C = 1.5m + 3.

The intercept

Where the line meets the cost axis: the fixed charge, paid even for 0 miles.

The gradient

The cost per mile: £1.50.

Not through the origin

A fixed charge means cost is NOT directly proportional to distance.

Reading off

8 miles: 1.5 × 8 + 3 = £15.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Comparing Two Deals

Graphs

Lesson 4 of 8

Phone plan A costs £20 a month plus 5p per minute. Plan B costs 15p per minute, with no monthly charge. For how many minutes do they cost the same? Which is cheaper for 300 minutes?

1

Write a formula for each

A: C = 20 + 0.05m; B: C = 0.15m

2

They cost the same where the lines cross

20 + 0.05m = 0.15m

3

Solve

20 = 0.1m, so m = 200

4

300 minutes

A: 20 + 15 = £35; B: £45

ANSWER

The same at 200 minutes; plan A is cheaper for 300 minutes.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Filling Containers

Graphs

Lesson 4 of 8

Water pours in at a steady rate. The graph of depth against time depends on the width of the container.

Straight sides

A cylinder or cuboid fills at a steady rate: a straight line.

Wider at the top

The depth rises quickly at first, then more slowly: a curve that gets less steep.

Narrower at the top

The depth rises slowly at first, then faster: a curve that gets steeper.

Wide then narrow parts

Each section of the container gives its own section of graph; a narrow section gives a steeper part.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Shape and Graph

Graphs

Lesson 4 of 8

Container

How the width changes

Graph of depth

Cylinder

Same width all the way up

Straight line

Vase, wide at the top

Gets wider

Curve, getting less steep

Cone, point up

Gets narrower

Curve, getting steeper

Flask: wide base, narrow neck

Wide, then narrow

Line, then a steeper line

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Graphs

Lesson 4 of 8

Conversion graph

A graph for changing between two units.

Fixed charge

A cost that is paid whatever the amount used; the y-intercept.

Direct proportion

Two quantities whose graph is a straight line through the origin.

Break-even point

Where two cost lines cross, so both options cost the same.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Graphs

Lesson 4 of 8

YOUR TASK

Which Taxi?

12 minutes

Taxi X charges £2 plus £2 per mile. Taxi Y charges £6 plus £1.50 per mile. Draw both graphs for 0 to 12 miles on the same axes. For which journeys is each taxi cheaper?

1

Make a table of values for each taxi.

2

Plot both lines on the same axes.

3

Find where they cross.

WHAT A GOOD ANSWER SHOWS

X: C = 2m + 2; Y: C = 1.5m + 6. They cross where 2m + 2 = 1.5m + 6, so m = 8 miles (£18). X is cheaper under 8 miles; Y is cheaper over 8 miles.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Graphs

Lesson 4 of 8

Read a conversion graph both ways.

Use a conversion graph for values off the scale.

Explain the gradient of a real-life graph.

Explain the intercept of a real-life graph.

Compare two options using graphs.

Match a container to its depth-time graph.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Conversion graph: straight line through the origin.

Cost graph: intercept = fixed charge; gradient = cost per unit.

Two lines cross where the options cost the same.

Narrow parts of a container fill faster: a steeper graph.

EXAM FOCUS

Plan A costs £20 a month plus 5p per minute. Plan B costs 15p per minute. Jo uses about 300 minutes a month. Which plan should she choose? (3 marks)

When asked what the gradient or intercept "represents", answer in context with units: "the cost per mile is £1.50", not just "the gradient is 1.5".

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