2-jun-14created by mr.lafferty maths dept drawing straight line graphs the gradient the gradient...

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

Drawing Straight line graphs

The gradient

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The gradient from coordinates

Int 2

The y intercept y = mx + c

Other forms / rearranging equation

Straight Line Straight Line GraphsGraphs


Starter QuestionsStarter Questionsw

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Q1. A house is valued at £50 000. Calculate its value after 4 years, if it appreciates by 5% each year.

Q2. Calculate 3.36 x 70 to 2 significant figures.

Int 2

Q3. Calculate the volume of a cylinder with radius 5cmand height 100 cm.

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

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1. To draw graphs by using a coordinate table

1.1. Understand the key points Understand the key points of drawing a straight line of drawing a straight line graphgraph

Int 2

2.2. Be able to plot a straight Be able to plot a straight line graphline graph


10 Apr 2023 Created by Mr. Lafferty Maths Dept

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y = x

y = 2x

y = 3x+1

y = x - 3

x

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Drawing Straight Line Graphs y = mx + c


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Int 2

Key Points

1.Make a table

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



Now try Exercise 1Odd numbersMIA (page 33)

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Int 2Straight Line Straight Line

GraphsGraphs



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-22.5 10Q1. Write this number in full to 1 sig. figs

Q2. Calculate the volume of the triangular prism.

Int 2

12cm

8cm

20cm


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2.2. Calculate simple Calculate simple gradients.gradients.

1. To explain how to calculate the gradient using right angled triangles

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

Int 2

The Gradient of a The Gradient of a LineLine


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The GradientThe GradientInt 2

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 -

coordinates


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0 2 4 6

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m = V = H

m = V = H

m = V = H

m = V = H


Round the classExercise 2

MIA (page 36)

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2.2. Calculate gradients Calculate gradients given two coordinates.given two coordinates.

1. To explain positive and negative gradients using coordinates.

1.1. Know gradient formula.Know gradient formula.

Int 2


mm = gradient = gradient

x1

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y-axis2 2(x ,y )

2 1y y

O x-axis

2 1x x

1 1(x ,y )

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The gradient The gradient using coordinatesusing coordinatesInt 2

x2

y2

y1

m = Y2 – Y1

X2 – X1

mm = gradient = gradient


y-axis(5,10)

O x-axis

(2,4)

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Find the gradient of the line.

m = Y2 – Y1

X2 – X1m = 10 – 4 5 – 2m = 6 = 2 3


y-axis

(3,8)

O x-axis

(1,2)


Find the gradient of the two lines.

(-3,8)

(-1,2)

m = Y2 – Y1

X2 – X1m = 8 - 2 3 - 1

m = 6 = 3 2

m = Y2 – Y1

X2 – X1m = 8 – 2 -3 – (-1)m = 6 = -3 -2


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Int 2

The gradient formula is :

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

The gradient The gradient using coordinatesusing coordinates

Gradient = m =

(y2 – y1)

(x2 – x1)


Exercise 3

Q1 – Q3MIA (page 37)

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Int 2

The gradient The gradient using coordinatesusing coordinates

Q1. Write out in full to 2 sig. figs.



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54.53 10

Q2. A superstore make 20% profit on each can of soup they sell. If they buy in a can for 50p.What is the selling price.

Q3. A hemisphere has a diameter of 10cm. Calculate its volume.

Int 2


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2.2. Identify the gradient Identify 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.

Int 2


10 Apr 2023 Created by Mr. Lafferty Maths Dept

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y = 2x + 1y = -x - 5

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Straight line equation and the gradient connection

m = -1 m = 2

2 1

2 1

m

y y

x x2 1

2 1

m

y y

x x


All straight lines have the equation of the form

y = mx + c

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Straight Line Straight Line EquationEquation

S4 Credit

Let’s investigate properties(You need GeoGebra to run link)


741 2 3 5 6 8 100

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y = mx + c

GradientWhere linemeets y-axis

y

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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


Now try Exercise 3 Q4 – Q9

MIA (page 38)

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Int 2


Q1. Write out in full to 1 significant fig.



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-51.58 10

Q2. A computer store buys in a laptop for £500.They want to make a 40% profit. How much do they sell it for.

Q3. A line is parallel to y = 2x. Write down its equation

Int 2



y = mx + c

Gradienty - intercept

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lines are parallel if

same gradient

y intercept is were line

cuts y axis

Slope left to right upwards

positive gradient

Slope left to right

downwards negative gradient


Now try Exercise 4

MIA (page 41 )

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Int 2




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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 answer

Int 2

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

xx -3-3 00 33

yy


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1. To show how to rearrange straight line equations into standard form and then identify the gradient and the y - intercept.

1.1. Be able to rearrange Be able to rearrange straight line equations.straight line equations.

y = y = mmx + x + cc

Int 2


2.2. Identify the gradientIdentify the gradient m m and y – intercept and y – intercept c c from from the standard form.the standard form.

y = y = mmx + x + cc


All straight lines have an equation of the form

y = mx + c

GradientWhere linemeets y-axis

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If two lines have the same gradient they are parallel.

y = 2x y = 2x+4

This is called

the standard

form


Rearrange the following straight line equations into standard form and identify the gradient and y-intercept.

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y – 3x = 4

2y – 2x = 6

y – x + 5 = 0

4y – 8 = 0

Standard form cm

y = 3x + 4

y = x + 3

y = x - 5

y = 2

3

1

1

0

4

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-5

2

Just a bit of algebra


Find the a line parallel to y – x = 0 and passing through (0,3).

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x – y = 0

Standard form cm

y = x 1 0

A line parallel to y = x has same gradient therefore m = 1Since it passes through (0,3) then c = 3

Using standard form line is y = x + 3


Now try Ex 5

MIA (page 45)

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Int 2Straight Line EquationStraight Line Equation

2-jun-14created by mr.lafferty maths dept drawing straight line graphs the gradient the gradient...

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