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2-Jun-14Created by Mr.Lafferty Maths Dept Drawing Straight line graphs The gradient www.mathsrevision.com The gradient from coordinates Int 2 The y intercept y = mx + c Other forms / rearranging equation Straight Line Graphs

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2-Jun-14Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com 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 5cm and height 100 cm.

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2-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 1.To draw graphs by using a coordinate table 1.Understand the key points of drawing a straight line graph Int 2 2.Be able to plot a straight line graph Straight Line Graphs

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2-Jun-14Created by Mr. Lafferty Maths Dept 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = x y = 2x y = 3x+1 y = x - 3 xyxy 0 0 3 3 -4 xyxy 0 0 3 6 -8 xyxy -2 -5 0 1 2 7 xyxy 0 -3 4 1 8 5 Drawing Straight Line Graphs y = mx + c

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2-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com Int 2 Key Points 1.Make a table 2.Calculate and plot 3 coordinates 3. Draw a line through points Straight Line Graphs

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2-Jun-14Created by Mr.Lafferty Maths Dept Now try Exercise 1 Odd numbers MIA (page 33) www.mathsrevision.com Int 2 Straight Line Graphs

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2-Jun-14Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com Q1.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-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Calculate simple gradients. 1.To explain how to calculate the gradient using right angled triangles 1.Gradient is : change in vertical height divided by change in horizontal distance Int 2 The Gradient of a Line

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2-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com The Gradient Int 2 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

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2-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com The Gradient Int 2 3 4 3 2 5 2 6 3 m = V = H m = V = H m = V = H m = V = H

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2-Jun-14Created by Mr.Lafferty Maths Dept Round the class Exercise 2 MIA (page 36) www.mathsrevision.com The Gradient Int 2

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2-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Calculate gradients given two coordinates. 1.To explain positive and negative gradients using coordinates. 1.Know gradient formula. Int 2 The Gradient of a Line

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m = gradient x1x1 2-Jun-14www.mathsrevision.com 13 y-axis O x-axis www.mathsrevision.com The gradient using coordinates Int 2 x2x2 y2y2 y1y1 m = Y 2 – Y 1 X 2 – X 1

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m = gradient 2-Jun-14www.mathsrevision.com 14 y-axis O x-axis www.mathsrevision.com The gradient using coordinates Int 2 Find the gradient of the line. m = Y 2 – Y 1 X 2 – X 1 m = 10 – 4 5 – 2 m = 6 = 2 3

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2-Jun-14www.mathsrevision.com 15 y-axis O x-axis The gradient using coordinates Int 2 Find the gradient of the two lines. m = Y 2 – Y 1 X 2 – X 1 m = 8 - 2 3 - 1 m = 6 = 3 2 m = Y 2 – Y 1 X 2 – X 1 m = 8 – 2 -3 – (-1) m = 6 = -3 -2

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2-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com 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 using coordinates Gradient = m = (y 2 – y 1 ) (x 2 – x 1 )

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2-Jun-14Created by Mr.Lafferty Maths Dept Exercise 3 Q1 – Q3 MIA (page 37) www.mathsrevision.com Int 2 The gradient using coordinates

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Q1.Write out in full to 2 sig. figs. 2-Jun-14Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com 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-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Identify 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. Int 2 The Gradient of a Line

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2-Jun-14Created by Mr. Lafferty Maths Dept 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = 2x + 1 y = -x - 5 xyxy 0 1 1 3 3 7 xyxy 0 -5 1 -6 3 -8 Straight line equation and the gradient connection m = -1m = 2

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2-Jun-14Created by Mr.Lafferty Maths Dept All straight lines have the equation of the form y = mx + c www.mathsrevision.com Straight Line Equation S4 Credit Lets investigate properties (You need GeoGebra to run link)

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2-Jun-14Created by Mr.Lafferty Maths Dept 74123568 10 0 1 2 3 4 5 6 7 8 9 9 x All straight lines have the equation of the form y = mx + c Gradient Where line meets y-axis y www.mathsrevision.com 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

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2-Jun-14Created by Mr.Lafferty Maths Dept Now try Exercise 3 Q4 – Q9 MIA (page 38) www.mathsrevision.com Int 2 The Gradient of a Line

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Q1.Write out in full to 1 significant fig. 2-Jun-14Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com 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

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2-Jun-14Created by Mr.Lafferty Maths Dept All straight lines have the equation of the form y = mx + c Gradient y - intercept www.mathsrevision.com Straight Line Equation 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

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2-Jun-14Created by Mr.Lafferty Maths Dept Now try Exercise 4 MIA (page 41 ) www.mathsrevision.com Int 2 Straight Line Graphs

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2-Jun-14Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com 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 answer Int 2 y = x + 2 and y = 2x + 2x-303y

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2-Jun-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 1.To show how to rearrange straight line equations into standard form and then identify the gradient and the y - intercept. 1.Be able to rearrange straight line equations. y = mx + c Int 2 Straight Line Equation 2.Identify the gradient m and y – intercept c from the standard form. y = mx + c

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2-Jun-14Created by Mr.Lafferty Maths Dept All straight lines have an equation of the form y = mx + c Gradient Where line meets y-axis www.mathsrevision.com Straight Line Equation If two lines have the same gradient they are parallel. y = 2xy = 2x+4 This is called the standard form

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2-Jun-14Created by Mr.Lafferty Maths Dept Rearrange the following straight line equations into standard form and identify the gradient and y-intercept. www.mathsrevision.com Straight Line Equation y – 3x = 4 2y – 2x = 6 y – x + 5 = 0 4y – 8 = 0 Standard formcm y = 3x + 4 y = x + 3 y = x - 5 y = 2 3 1 1 0 4 3 -5 2 Just a bit of algebra

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2-Jun-14Created by Mr.Lafferty Maths Dept Find the a line parallel to y – x = 0 and passing through (0,3). www.mathsrevision.com Straight Line Equation x – y = 0 Standard formcm y = x10 A line parallel to y = x has same gradient therefore m = 1 Since it passes through (0,3) then c = 3 Using standard form line isy = x + 3

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2-Jun-14Created by Mr.Lafferty Maths Dept Now try Ex 5 MIA (page 45) www.mathsrevision.com Int 2 Straight Line Equation

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