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Drawing Straight line graphs The gradient from Coordinates General Equation y = mx + c S4 Credit Equation from 2 Points Best – fitting straight line Straight Line Graphs Modelling Situations The gradient Vertical ÷ Horizontal Exam Type Questions

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11-May-15Created by Mr.Lafferty Maths Dept Starter Questions Q1.Calculate 7 – 5 x 2 Q2.Calculate S4 Credit Q3.Is this triangle right angled ? Explain

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11-May-15Created by Mr.Lafferty Maths Dept Learning Intention Success Criteria 1.To show how to get the equations for horizontal and vertical lines. 1.Understand that vertical lines have equations of the form x = a The Gradient of a Line S4 Credit 2.Understand that horizontal lines have equations of the form y = a

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x y May-15Created by Mr. Lafferty Maths Dept x = y = Equations for Vertical and Horizontal lines Mark the points on your grid below and then join them together Vertical lines have equations of the form 8 Horizontal lines have equations of the form 2 x =-6 y =-9

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11-May-15Created by Mr.Lafferty Maths Dept Now Try MIA Exercise 2.1 Ch7 (page 136) The Gradient S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Starter Questions Q1.Write this number in full to 1 sig. figs Q2.Calculate the volume of the triangular prism. 12cm 8cm 20cm S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Learning Intention Success Criteria 2.Calculate simple gradients. 1.To explain how to calculate the gradient using a right angle triangle 1.Gradient is : change in vertical height divided by change in horizontal distance The Gradient of a Line S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept The Gradient Change in vertical height Change in horizontal distance The gradient is the measure of steepness of a line The steeper a line the bigger the gradient Difference in x -coordinates Difference in y -coordinates S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept The Gradient S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Now Try MIA Exercise 3.1 Ch7 (page 139) The Gradient S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Starter Questions Q1.A house 4 years ago is valued at £ Calculate it’s value if it has increased by 5%. Q2.Calculate 3.36 x 70 to 2 significant figures. Q3.Write down the 3 ways of factorising. S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Learning Intention Success Criteria 2.Calculate gradients given two coordinates. 1.To explain positive and negative gradients using coordinates. 1.Know gradient formula. The Gradient of a Line S4 Credit

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m = gradient x1x1 11-May-15www.mathsrevision.com 13 y-axis O x-axis The gradient using coordinates x2x2 y2y2 y1y1 S4 Credit

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m = gradient 11-May-15www.mathsrevision.com 14 y-axis O x-axis The gradient using coordinates Find the gradient of the line. S4 Credit

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11-May-15www.mathsrevision.com 15 y-axis O x-axis The gradient using coordinates Find the gradient of the two lines. S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept 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 using coordinates S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Now try MIA Ex 4.2 Ch7 (page 143) The gradient using coordinates S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Learning Intention Success Criteria 1.To draw graphs by using a coordinate table 1.Understand the keypoints of drawing a straight line graph 2.Be able to plot a straight line graph Straight Line Graphs S4 Credit

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11-May-15Created by Mr. Lafferty Maths Dept x y y = x y = 2x y = 3x+1 y = x - 3 xyxy xyxy xyxy xyxy Drawing Straight Line Graphs y = ax + b

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11-May-15Created by Mr.Lafferty Maths Dept Key Points 1.Make a table 2.Calculate and plot 3 coordinates 3. Draw a line through points Straight Line Graphs S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Now try MIA Ex5.1 Q5 Only Ch7 (page 145) Straight Line Graphs S4 Credit

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Q1.Write out in full to 2 sig. figs. 11-May-15Created by Mr.Lafferty Maths Dept Starter Questions 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. Explain why 4x 2 – 16 = 4(x + 2)( x – 2) S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Learning Intention Success Criteria 2.Identity the gradient m from the standard form. 1.To explain the connection between the straight line equation and the gradient. 1.Understand the term standard form. The Straight Line Equation S4 Credit

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11-May-15Created by Mr. Lafferty Maths Dept x y y = 2x + 1 y = -x - 5 xyxy xyxy Straight line equation and the gradient connection m = -1m = 2

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11-May-15Created by Mr.Lafferty Maths Dept All straight lines have the equation of the form y = mx + c Straight Line Equation S4 Credit Let’s investigate properties (You need GeoGebra to run link)

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11-May-15Created by Mr.Lafferty Maths Dept x All straight lines have the equation of the form y = mx + c Gradient Where line meets y-axis y Straight Line Equation Find the equations of the following lines y = xy = x+4 lines are parallel if they have the same gradient y = 4x+2 y = -0.5x+2 S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Now try MIA Ex 6.1 Ch7 (page 146) The Gradient of a Line S4 Credit

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Q1.Write out in full to 1 significant fig. 11-May-15Created by Mr.Lafferty Maths Dept Starter Questions 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 S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept All straight lines have the equation of the form y = mx + c Gradient y - intercept Straight Line Equation 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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11-May-15www.mathsrevision.com Equation of a Straight Line To find the equation of a straight line we need to know Two points that lie on the line ( x 1, y 1 ) and ( x 2, y 2 ) Or The gradient and a point on the line m and (a,b) y = mx+c S4 Credit

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Find the equation of the straight line passing through the points (4, 4) and (8,24). Solution y = mx+c S4 Credit Equation of a Straight Line Using the point (4,4) and the gradient m = 5 sub into straight line equation 4 = 5 x 4 + cc = = -16 Equation : y = 5x - 16 y = mx + c

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Find the equation of the straight line passing through the points (3, -5) and (6,4). Solution y = mx+c S4 Credit Equation of a Straight Line Using the point (6,4) and the gradient m = 3 sub into straight line equation 4 = 3 x 6 + cc = = -14 Equation : y = 3x - 14 y = mx + c

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11-May-15Created by Mr.Lafferty Maths Dept Now try MIA Ex 6.2 Ch7 (page 147 ) Straight Line Graphs S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Starter Questions Q1.The points ( 1, 4) and (3, 11) lie on a line. 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-303 y S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Learning Intention Success Criteria 1.How to model real life situations using straight line theory 1.Be able to work out gradient and y intercept using a graph. Modelling Using Straight Line Equation 2.Form an equation for any straight line graph. S4 Credit

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Modelling Real – life 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) 30 C = 30 T+ 10 (d)Find the cost for a plumber for 10 hours? T = 10C = 10 x = £130

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80 -5 Modelling Real – life The graph shows how a the volume of water tank drains over time. (a)Calculate the gradient. (b)What is the value of V when T = 0 (c)Write down an equation connecting V and T. Pick any 2 points (8,40) (0,80) 80 V =T+ (d)How long before the tank is empty? V = 00 = -5 x T + 80T = (-80) ÷(–5) = 16mins

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11-May-15Created by Mr.Lafferty Maths Dept Now try Ex 7.1 MIA (page 149) Straight Line Equation S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Starter Questions Q1.The points ( 5, 7) and (7, 21) lie on the same line. Find the gradient of the line. Q2. Complete the table given :y = 2x + 10 Q3.Are the two lines parallel. Explain answer y = -2x + 1 and y = 2x + 1 x-303 y S4 Credit

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11-May-15Created by Mr.Lafferty Maths Dept Learning Intention Success Criteria 1.How to model real life situations using straight line theory 1.Be able to work out gradient and y intercept using a graph. Best Fit Straight Line Equation 2.Form an equation for any straight line graph. S4 Credit

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x c = 0 (b)Draw in the best-fit line and find an equation relating height and weight Best-Fitting Straight line Data was collected on pupils weight and height. Data is plotted below. (a)Is there correlation between height and weight. Pick any 2 points (70,180) h =w+ (d)What height is a pupils who weights 40 kgs? w = 40h = 2.57 x 40 = cms x (0,0) Yes, a positive correlation

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c = (b)Draw in the best-fit line and find an equation relating value and year. Best-Fitting Straight line A survey was carried out on the value of cars depending on their age The data is plotted below. (a)Is there correlation between value and age. Pick any 2 points (8,8) v =y+ (d)What is the cost of a car after 4years? y = 4v = x = 13 x (0,18) Yes, a negative correlation x Value = £13 000

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11-May-15Created by Mr.Lafferty Maths Dept Now try Ex 8.1 MIA (page 151) S4 Credit Best Fit Straight Line Equation

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Example The graph shows an electrician’s charging system. He has a call-out charge plus an hourly rate. a) Work out the equation of the line. b) Calculate the cost of a 10 hour job. S4 Credit Exam Type Straight Line Questions

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Exam Type Straight Line Questions a) Pick two convenient points on the line, say (0, 30) and (5, 80). Thinking of the form y = mx + c The y-intercept gives c = 30 = 10 The equation is: y = 10x + 30 The label on the y-axis is C and the label on the x-axis is T So the equation is C = 10 T + 30 So the equation is C = 10 T + 30 b) Find C when T = 10 C = 10 x = 130 The cost of a 10 hr job is £130. S4 Credit

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1. The tank of a car contains 5 litres of petrol. The graph below shows how the volume of petrol in this tank changes as a further 45 litres of petrol is pumped in at a steady rate for 60 seconds. Find the equation of the straight line in terms of V and t. S4 Credit Exam Type Straight Line Questions

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In the diagram below. A is the point (-1, -7) and B is the point (4, 3). 2. (a) Find the gradient of the line AB. (b) AB cuts the y-axis at the point (0, -5). Write down the equation of the line AB. (c) The point (3k, k) lies on the line AB. Find the value of k. S4 Credit Exam Type Straight Line Questions

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A water pipe runs between two buildings. These are represented by the points A and B in the diagram below. 3. (a) Using the information in the diagram, show that the equation of the line AB is 3y – x = 6. S4 Credit Exam Type Straight Line Questions

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(b)An emergency outlet pipe has to be built across the main pipe. The line representing this outlet pipe has equation 4y + 5x = 46. Calculate the coordinates of the point on the diagram at which the outlet pipe will cut across the main water pipe. S4 Credit Exam Type Straight Line Questions

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S4 Credit Exam Type Straight Line Questions

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