Basic Lines Drawing Straight Lines y = ax S4 Straight Line Graphs The gradient Vertical ÷...

Basic Lines

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Drawing Straight Lines y = ax

S4

Straight Line Straight Line GraphsGraphs

The gradient Vertical ÷ Horizontal

Drawing Straight Lines y =ax + b

11 Apr 202311 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept

Starter QuestionsStarter Questionsw

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Q2. Calculate

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2 12 1

5 2

98

5

Q3. Is this triangle right angled ?Explain

11 Apr 202311 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww

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2.2. Calculate simple Calculate simple gradients.gradients.

1. To explain how to calculate the gradient using a right angle triangle

1.1. Gradient is : Gradient is : change in vertical height change in vertical height

divided by divided by change in horizontal change in horizontal

distancedistance

The Gradient of a The Gradient of a LineLine

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The GradientThe Gradient

Change in vertical height

Change in horizontal distance

The gradient is the measure of steepness of a line

V

H

The steeper a line the bigger the gradientDifference in x -

coordinates

Difference in y -

coordinatesS4


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The GradientThe Gradient

0 2 4 6

2

4

6

-6

- 4

-2

-2- 4-6

V

mH

3

4

V

mH

3

2

V

mH 5

V

mH

2

6

1

3

3

S4


Now Try MIAExercise 1

Ch6 (page 64)

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The GradientThe GradientS4



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Expand and simplify 4( 3 + 2x) – 3(x + 1)

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1. To explain the keypoints of straight line graphs that pass through the origin and write down its equation.

1.1. Understand the keypoints Understand the keypoints of straight line graph of straight line graph passing through the origin.passing through the origin.

2.2. Be able to write down Be able to write down equation of a straight line equation of a straight line passing through the passing through the origin.origin.


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11 Apr 2023 Created by Mr. Lafferty Maths Dept

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

y = x

y = 2x

y = 3x

y = 0.5x

x

y

0

0

2

2

6

6

x

y

0

0

3

6

4

8

x

y

0

0

1

3

2

6

x

y

0 0

4

2

8

4

Straight Line Graphs y = ax


Now tryEx2

Ch6 (page 68)

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Straight Line Straight Line GraphsGraphsS4

Q1. Calculate 40 – 30x2



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2.2. Identity the gradient Identity the gradient mm from the standard form.from the standard form.

1. To explain the connection between the straight line equation and the gradient.

1.1. Understand the term Understand the term standard form.standard form.

The Straight Line Equation

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1.Make a table

2.Calculate and plot 3 coordinates 3. Draw a line through points


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0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

y = x

y = 2x

y = 3x

y = 5x

x

y

0

0

2

2

6

6

x

y

0

0

3

6

4

8

x

y

0

0

1

3

2

6

x

y

0 0

1

5

2

10

Drawing Straight Line Graphs y = ax


Now try Ex 3 Ch6 (page 70)

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The Gradient of a The Gradient of a LineLine

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Factorise 5x + 10

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1. To explain the draw straight lines of the form y = ax + b.

1.1. Be able to draw straight Be able to draw straight lines of the form y = ax + blines of the form y = ax + b

The Straight Line Equation

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1.Make a table

2.Calculate and plot 3 coordinates 3. Draw a line through points


S4


0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

y = x

y = 2x + 3

y = 3x+1

y = x - 3

x

y

0

0

2

2

4

4

x

y

0

3

1

5

2

7

x

y

0

1

1

4

2

7

x

y

0

-3

4

1

8

5

Drawing Straight Line Graphs y = ax + b


741 2 3 5 6 8 100

1

2

3

4

5

6

7

8

9

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9 x

All straight lines have the equation of the form

y = mx + c

GradientWhere linemeets y-axis

y

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Straight Line Straight Line EquationEquation

Find the equations of the following lines

y = x y = x+4

lines are parallel if they have the same gradient

y = 4x+2 y = -0.5x+2

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Now try MIAEx 4

Ch6 (page 73)

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Straight Line Straight Line EquationEquation

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Basic Lines Drawing Straight Lines y = ax S4 Straight Line Graphs The gradient Vertical ÷...

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