Representing inequalities graphically.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Representing inequalities graphically

Equations and graphs

Lesson 2 of 6

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up

Equations and graphs

Lesson 2 of 6

Answer each one, then check.

1

What does x > 3 mean?

2

What does y ≤ 2 mean?

3

What is the line x = 4?

4

What is the line y = 2?

5

Draw the line y = x: what is its gradient?

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up - Answers

Equations and graphs

Lesson 2 of 6

1

What does x > 3 mean?

x is greater than 3

2

What does y ≤ 2 mean?

y is less than or equal to 2

3

What is the line x = 4?

A vertical line through 4 on the x-axis

4

What is the line y = 2?

A horizontal line through 2 on the y-axis

5

Draw the line y = x: what is its gradient?

1

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Equations and graphs

Lesson 2 of 6

1

Draw a boundary line for an inequality.

2

Choose a solid or dashed line.

3

Shade the correct region.

4

Write inequalities for a region and list integer points.

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Equations and graphs

Lesson 2 of 6

INEQUALITY REGIONS

An inequality describes a region. Draw the boundary line, then shade the side where the inequality is true.

Solid line for ≤ or ≥. Dashed line for < or >.

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

A Region from Three Inequalities

Equations and graphs

Lesson 2 of 6

The region R satisfies all three inequalities.

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Solid or Dashed?

Equations and graphs

Lesson 2 of 6

The boundary is part of the region only for ≤ and ≥.

Inequality

Boundary line

Points on the line

y ≥ 2

Solid

Included

y > 2

Dashed

Not included

x + y ≤ 6

Solid

Included

y < x

Dashed

Not included

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Test a Point

Equations and graphs

Lesson 2 of 6

Show which side of the line x + y = 6 satisfies x + y ≤ 6.

1

Test the origin

0 + 0 = 0

2

Compare

0 ≤ 6 is true

3

So shade

The side of the line containing the origin

ANSWER

Shade the region below the line x + y = 6, including the line.

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Integer Points in a Region

Equations and graphs

Lesson 2 of 6

List the integer points in x ≥ 1, y ≥ 1, x + y ≤ 4.

1

Try x = 1

y = 1, 2, 3

2

Try x = 2

y = 1, 2

3

Try x = 3

y = 1

ANSWER

(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Writing Inequalities

Equations and graphs

Lesson 2 of 6

A region is bounded by y = 1, x = 4 and y = x, and lies above y = 1, to the left of x = 4 and below y = x. Write the inequalities.

1

Above y = 1

y ≥ 1

2

Left of x = 4

x ≤ 4

3

Below y = x

y ≤ x

ANSWER

y ≥ 1, x ≤ 4, y ≤ x

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Tips

Equations and graphs

Lesson 2 of 6

Keep it clear.

Label R

Mark the required region clearly.

Check with a point

Test one point in the region in every inequality.

Boundary lines

Draw all lines even if only part of them bounds the region.

Read the instruction

Some questions ask you to shade the region that is NOT wanted.

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

Equations and graphs

Lesson 2 of 6

Inequality

A statement using <, >, ≤ or ≥.

Boundary

The line separating the region from the rest.

Region

The set of points that satisfy the inequalities.

Integer

A whole number.

Test point

A point used to decide which side to shade.

Solid line

Boundary included.

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Equations and graphs

Lesson 2 of 6

YOUR TASK

Sketch the Region

12 minutes

Draw the region satisfying x ≥ 2, y ≥ 1 and x + y ≤ 6. List the integer points that lie in it.

1

Draw each boundary line.

2

Count integer points column by column.

WHAT A GOOD ANSWER SHOWS

The region is a triangle with corners (2, 1), (5, 1) and (2, 4). Integer points: (2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(4,1),(4,2),(5,1).

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

Equations and graphs

Lesson 2 of 6

Draw x = a and y = b lines.

Draw sloping boundary lines.

Use solid and dashed lines.

Test a point.

Shade the correct region.

Write inequalities for a region.

List integer points.

Label R clearly.

openrevise.com

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

≤ and ≥: solid line. < and >: dashed.

Test a point to decide which side to shade.

The region satisfies all inequalities at once.

Integer points on a solid boundary are included.

EXAM FOCUS

The diagram shows a region R. Write down the three inequalities that define R. (3 marks)

Name each boundary line first, then decide which side is R.

openrevise.com