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**Created by Mr.Lafferty Maths Dept**

Straight Line Graphs Int 2 Drawing Straight line graphs The gradient The gradient from coordinates The y intercept y = mx + c Other forms / rearranging equation 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Starter Questions Int 2 Q1. A house is valued at £ Calculate its value after 4 years, if it appreciates by 5% each year. Q2. Calculate 3.36 x 70 to 2 significant figures. Q3. Calculate the volume of a cylinder with radius 5cm and height 100 cm. 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Straight Line Graphs Int 2 Learning Intention Success Criteria To draw graphs by using a coordinate table Understand the key points of drawing a straight line graph Be able to plot a straight line graph 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Drawing Straight Line Graphs y = mx + c y = x**

1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y x y 3 -4 y = 3x+1 3 -4 x y -2 2 -5 1 7 y = x - 3 y = 2x x y 4 8 x y 3 -4 -3 1 5 6 -8 31-Mar-17 Created by Mr. Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Straight Line Graphs Int 2 Key Points Make a table Calculate and plot 3 coordinates 3. Draw a line through points 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Straight Line Graphs Int 2 Now try Exercise 1 Odd numbers MIA (page 33) 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Starter Questions Int 2 Q1. Write this number in full to 1 sig. figs Q2. Calculate the volume of the triangular prism. 20cm 12cm 8cm 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**The Gradient of a Line www.mathsrevision.com Learning Intention**

Success Criteria To explain how to calculate the gradient using right angled triangles Gradient is : change in vertical height divided by change in horizontal distance 2. Calculate simple gradients. 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

The Gradient Difference in y -coordinates Int 2 The gradient is the measure of steepness of a line Change in vertical height Change in horizontal distance Difference in x -coordinates The steeper a line the bigger the gradient 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

The Gradient Int 2 3 m = V = H 4 3 m = V = H 2 3 m = V = H 5 2 m = V = H 6 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

The Gradient Int 2 Round the class Exercise 2 MIA (page 36) 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

The Gradient of a Line Int 2 Learning Intention Success Criteria To explain positive and negative gradients using coordinates. Know gradient formula. 2. Calculate gradients given two coordinates. 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**The gradient using coordinates**

Mr. Lafferty The gradient using coordinates Int 2 m = gradient y-axis m = Y2 – Y1 X2 – X1 y2 We start by find the equation of a circle centre the origin. First draw set axises x,y and then label the origin O. Next we plot a point P say, which as coordinates x,y. Next draw a line from the origin O to the point P and label length of this line r. If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O. Remembering Pythagoras’s Theorem from Standard grade a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin. y1 O x-axis x1 x2 31-Mar-17

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**The gradient using coordinates**

Mr. Lafferty The gradient using coordinates Int 2 Find the gradient of the line. m = gradient y-axis m = Y2 – Y1 X2 – X1 m = 10 – 4 5 – 2 We start by find the equation of a circle centre the origin. First draw set axises x,y and then label the origin O. Next we plot a point P say, which as coordinates x,y. Next draw a line from the origin O to the point P and label length of this line r. If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O. Remembering Pythagoras’s Theorem from Standard grade a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin. m = 6 = 2 3 O x-axis 31-Mar-17

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**The gradient using coordinates**

Mr. Lafferty The gradient using coordinates Int 2 Find the gradient of the two lines. y-axis m = Y2 – Y1 X2 – X1 m = Y2 – Y1 X2 – X1 m = 3 - 1 m = 8 – 2 -3 – (-1) We start by find the equation of a circle centre the origin. First draw set axises x,y and then label the origin O. Next we plot a point P say, which as coordinates x,y. Next draw a line from the origin O to the point P and label length of this line r. If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O. Remembering Pythagoras’s Theorem from Standard grade a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin. m = 6 = -3 -2 m = 6 = 3 2 O x-axis 31-Mar-17

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**The gradient using coordinates**

Int 2 The gradient formula is : Gradient = m = (y2 – y1) (x2 – x1) 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 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**The gradient using coordinates**

Int 2 Exercise 3 Q1 – Q3 MIA (page 37) 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Starter Questions Int 2 Q1. Write out in full to 2 sig. figs. 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. 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

The Gradient of a Line Int 2 Learning Intention Success Criteria To explain the connection between the straight line equation and the gradient. Understand the term standard form. 2. Identify the gradient m from the standard form. 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr. Lafferty Maths Dept**

Straight line equation and the gradient connection 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y y = -x - 5 y = 2x + 1 x y 1 3 x y 1 3 -5 -6 -8 1 3 7 m = -1 m = 2 31-Mar-17 Created by Mr. Lafferty Maths Dept

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**Straight Line Equation**

S4 Credit All straight lines have the equation of the form y = mx + c Let’s investigate properties (You need GeoGebra to run link) 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Straight Line Equation**

y 10 lines are parallel if they have the same gradient All straight lines have the equation of the form 9 8 y = mx + c 7 6 5 4 3 Where line meets y-axis 2 Gradient 1 x 1 2 3 4 5 6 7 8 9 10 Find the equations of the following lines y = x y = x+4 y = 4x+2 y = -0.5x+2 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

The Gradient of a Line Int 2 Now try Exercise 3 Q4 – Q9 MIA (page 38) 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Starter Questions Int 2 Q1. Write out in full to 1 significant fig. 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 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Straight Line Equation**

lines are parallel if same gradient Straight Line Equation All straight lines have the equation of the form Slope left to right upwards positive gradient y = mx + c y - intercept Gradient y intercept is were line cuts y axis Slope left to right downwards negative gradient 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Straight Line Graphs Int 2 Now try Exercise 4 MIA (page 41 ) 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Created by Mr.Lafferty Maths Dept**

Starter Questions Int 2 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 x -3 3 y Q3. Are the two lines parallel. Explain answer y = x and y = 2x + 2 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Straight Line Equation**

Int 2 Learning Intention Success Criteria To show how to rearrange straight line equations into standard form and then identify the gradient and the y - intercept. Be able to rearrange straight line equations. y = mx + c Identify the gradient m and y – intercept c from the standard form. y = mx + c 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Straight Line Equation**

This is called the standard form Straight Line Equation All straight lines have an equation of the form y = mx + c Where line meets y-axis Gradient If two lines have the same gradient they are parallel. y = 2x y = 2x+4 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Straight Line Equation**

Just a bit of algebra Straight Line Equation Rearrange the following straight line equations into standard form and identify the gradient and y-intercept. Standard form m c y – 3x = 4 y = 3x + 4 3 4 2y – 2x = 6 y = x + 3 1 3 y – x + 5 = 0 y = x - 5 1 -5 4y – 8 = 0 y = 2 2 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Straight Line Equation**

Find the a line parallel to y – x = 0 and passing through (0,3). Standard form m c x – y = 0 y = x 1 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 is y = x + 3 31-Mar-17 Created by Mr.Lafferty Maths Dept

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**Straight Line Equation**

Int 2 Now try Ex 5 MIA (page 45) 31-Mar-17 Created by Mr.Lafferty Maths Dept

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