15-Feb-14Created by Mr.Lafferty Maths Dept The Gradient Change in vertical height Change in horizontal distance The gradient is the.

10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww

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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 Credit


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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 Credit

mm = gradient = gradient

x1

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y-axis2 2(x ,y )

2 1

2 1

y yx

mx

2 1y y

O x-axis

2 1x x

1 1(x ,y )

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The gradient The gradient using coordinatesusing coordinates

x2

y2

y1

S4 Credit

mm = gradient = gradient


y-axis(5,10)

2 1

2 1

y yx

mx

O x-axis

(2,4)

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Find the gradient of the line.

10 4

5 2m

6

23

m

S4 Credit

2 1

2 1

y yx

mx

8 2

3 ( 1)m

6

32

m


y-axis

(3,8) 2 1

2 1

y yx

mx

O x-axis

(1,2)


Find the gradient of the two lines.

8 2

3 1m

6

32

m

(-3,8)

(-1,2)

S4 Credit


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2 1

2 1

= m

y ygradient

x x

It is a measure of how steep a line is

A line sloping up from left to right is a positive gradient

A line sloping down from left to right is a negative gradient


S4 Credit


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1.Make a table

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

Straight Line Straight Line GraphsGraphs

S4 Credit

10 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+1

y = x - 3

x

y

0

0

3

3

-4

-4

x

y

0

0

3

6

-4

-8

x

y

-2

-5

0

1

2

7

x

y

0

-3

4

1

8

5

Drawing Straight Line Graphs y = ax + b


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 = 2x + 1y = 2x - 5

x

y

0

1

1

3

3

7

x

y

0

-5

1

-3

3

1

Straight line equation and the gradient connection

m = 2 m = 2

2 1

2 1

m

y y

x x2 1

2 1

m

y y

x x

10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept

741 2 3 5 6 8 100

1

2

3

4

5

6

7

8

9

10

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

S4 Credit

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


x =

y =

Equations for Vertical and Horizontal lines

Mark the pointson your grid belowand then join them together

Vertical lines have equations of the form

8Horizontal lines have equations of the form

2

x = -6

y = -9


All straight lines have the equation of the form

y = mx + c

Gradienty - intercept

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Straight Line Straight Line EquationEquation

y intercept is were line

cuts y axis

Slope left to right upwards

positive gradient

Slope left to right

downwards negative gradient

S4 Credit

lines are parallel if

same gradient

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Equation of a Straight Line

To find the equation of a straight line we need to know

Two points that lie on the line

( x1, y1) and ( x2, y2)

Or

The gradient and a point on the line

m and (a,b)

y = mx+c

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S4 Credit

Find the equation of the straight line passing through the points (4, 4) and (8,24).

Solution2 1

2 1

y y 24 4 20m 5

x x 8 4 4

y = mx+c

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S4 Credit


Using the point (4,4) and the gradient m = 5 sub into straight line equation

4 = 5 x 4 + c c = 4 - 20 = -16

Equation :y = 5x - 16

y = mx + c

Find the equation of the straight line passing through the points (3, -5) and (6,4).

Solution3

39

365)(4

xxyy

m12

12

y = mx+c

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S4 Credit


Using the point (6,4) and the gradient m = 3 sub into straight line equation

4 = 3 x 6 + c c = 4 - 18 = -14

Equation :y = 3x - 14

y = mx + c


Starter QuestionsStarter Questionsw

ww

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Find the gradient of the line.

Q2. Complete the table given : y = 3x + 1

Q3. Are the two lines parallel. Explain your answer

y = x + 2 and y = 2x + 2

x -3 0 3

y

S4 Credit

Modelling Real – life

0 1 2 3 4 5 6 7 8 9 10 T

C

10

20

30

40

50

60

70

80

90

100

Cost

£Time

(hours)

The cost for hiring a plumber per hour is shown below

(a) Calculate the gradient.

(b) What is the value of C when T = 0

(c) Write down an equation connecting C and T.

Pick any 2 points

(7,100)

(0,30)

2 1

2 1

y ym

x x

100 307 0

10

30

C =

30

T +

10

(d) Find the cost for a plumber for 10 hours?

T = 10 C = 10x10 + 30 = £130

15-Feb-14Created by Mr.Lafferty Maths Dept The Gradient Change in vertical height Change in horizontal distance The gradient is the.

Documents

line x

gradient slide

y s4 credit slide

yaxis y

straight line graphs

form y

c gradient y intercept

solution y