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**Starter Activity: Guess the Rule**

y = mx + c Starter Activity: Guess the Rule x y x y 2 -2 1 4 1 1 2 6 2 4 3 8 3 7 -4 6 -4 -14 y = 2x + 2 y = 2x + 1

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**Starter Activity: Guess the Rule**

y = mx + c Starter Activity: Guess the Rule x y x y 3 33 2 10 4 43 4 18 5 53 6 26 6 63 8 34 -4 -37 -4 -14 y = 10x + 3 y = 4x + 2

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**Starter Activity: Guess the Rule**

y = mx + c Starter Activity: Guess the Rule x y x y 20 96 2 21 101 1 22 106 2 -2 23 111 3 -4 -4 24 -4 10 y = 5x - 4 y = -2x + 2

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**OBJECTIVE: By the end of the lesson you should…**

…be able to … … find the equation for any linear graph from the diagram (All pupils) … find the equation of any line given any two points on the line (Most pupils) … use these skills to interpret real life problems (Some pupils)

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**Straight Line Graphs (y = mx + c)**

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs (y = mx + c) m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c ch y = 2 ch x = 1 y = 2x + 3 y intercept = 3 The gradient is defined as the Change in y Change in x

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**Straight Line Graphs (y = mx + c)**

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs (y = mx + c) m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c ch y = 3 y = 3x - 4 ch x = 1 The gradient is defined as the Change in y Change in x y intercept = -4

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**Straight Line Graphs (y = mx + c)**

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs (y = mx + c) m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c y = ½x + 1 ch y = 1 ch x = 2 y intercept = 1 The gradient is defined as the Change in y Change in x

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**Straight Line Graphs (y = mx + c)**

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs (y = mx + c) m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c The gradient is defined as the Change in y Change in x ch y = 1 ch x = 3 y intercept = -5

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**Straight Line Graphs (y = mx + c)**

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs (y = mx + c) m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c ch y = 3 ch x = 4 y intercept = 2 The gradient is defined as the Change in y Change in x

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**Straight Line Graphs (y = mx + c)**

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y Straight Line Graphs (y = mx + c) m gives the gradient of the line and c gives the y intercept. All straight line graphs are of the form y = mx + c y intercept = 3 ch y = 4 ch x = 5 The gradient is defined as the Change in y Change in x

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**Key Questions: Find the formulae for these Real Life Problems**

(1) A taxi firm has a formula for working out fares It is in the form P=mN + c P=Price N = No. miles A 0 mile journey costs £2 A 2 miles journey costs £6 (2) A taxi firm has a formula for working out fares It is in the form P=mN + c P=Price N = No. cards 60 cards cost £ cards cost £255 Hint: If it helps then quickly sketch the graphs with N going across and P going up

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**OBJECTIVE: Have you met your lesson objectives?**

Are you able to … … find the equation for any linear graph from the diagram (All pupils) … find the equation of any line given any two points on the line (Most pupils) … use these skills to interpret real life problems (Some pupils)

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Factor P 16 8(8-5ab) 4(d² + 4) 3rs(2r – s) 15cd(1 + 2cd) 8(4a² + 3b²)

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