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2 Warm Up 1. Rotations can occur in a__________ or _____________ direction. Clockwise; counterclockwise 2. Unit circle moves in a ___________direction. Counterclockwise degrees - Two____ degree angles. 30 degrees 3. A half circle of rotation is ___and a quarter circle is _____. 180°; 90° 4. An object and its rotation are the same______ and size, but the figures may be turned in different_________. Shape; directions.

Copyright © Ed2Net Learning Inc. 3 Lets review what we have learned in the last lesson An object and its rotation are the same shape and size, but the figures may be turned in different directions. The rotation of an object is called its image. Rotations can occur in either a clockwise or counterclockwise direction. Rotation notation is usually denoted R( center, degrees ) 360 degrees is a full circle of rotation.

Copyright © Ed2Net Learning Inc. 4 R 90 (x,y) = ( -y, x) R 180 (x, y) = ( -x, -y) R 270 (x,y) = (y, -x) A rotation of 180º is also called a point reflection in the origin. Rotations > 0 are counterclockwise. Rotations < 0 are clockwise. Rotation Angle

Copyright © Ed2Net Learning Inc. 5 What is an equation: First let us understand meaning of equation Equation is an expression in which both the sides are equal Examples: 9= =8 2x=3

Copyright © Ed2Net Learning Inc. 6 An equation is like a balance scale because it shows that two quantities are equal. Look at the scale and equations below it. 2 lb 1lb 3 lb 2 =21+3 =1+3

Copyright © Ed2Net Learning Inc. 7 What is a linear equation: A linear equation is an equation which has got one or two variables. The highest power the variable is one. The linear equation in one variable will be always in the following standard form Ax + B=0, where A≠0 Where A and B are both constants

Copyright © Ed2Net Learning Inc. 8 Solving a linear equation A solution is that value of the unknown which satisfies the equation. For example: 3+x =5 So, x =2 is the solution of this equation because it satisfies this equation.

Copyright © Ed2Net Learning Inc. 9 METHOD OF SOLVING LINEAR EQUATIONS USE OF ADDITION AND SUBSTRACTION Addition property of equality  If there are 3 real numbers x, y and z and x=y then x + z = y + z Subtraction property of equality  As mentioned above if x=y then x - z = y - z

Copyright © Ed2Net Learning Inc. 10 Solve the equation: x – 5 = 10 We will use addition property here. x – 5 = 10 Add 5 to each side to get the variable on one side of the equal sign. x = x = 15 Check: To check your solution substitute your answer in the given equation.

Copyright © Ed2Net Learning Inc. 11 Examples Solve the equation: x + 2 = 14 We will use subtraction property here. x +2 = 14 Subtract 2 to each side to get the variable on one side of the equal sign. x = x = 12 Check: To check your solution substitute your answer in the given equation.

Copyright © Ed2Net Learning Inc. 12 METHOD OF SOLVING LINEAR EQUATIONS USE OF MULTIPLICATION AND DIVISION Multiplication property of equality  If there are 3 real numbers x, y and z and x=y then x * z = y * z Division property of equality  As mentioned above if x=y then x / z = y / z

Copyright © Ed2Net Learning Inc. 13 Solve the equation: y/5 = 20 We will use multiplication property here. y/5 = 20 Multiply 5 to each side to get the variable on one side of the equal sign. (y/5)×5 =20×5 y = 100 Check: To check your solution substitute your answer in the given equation.

Copyright © Ed2Net Learning Inc. 14 Solve the equation: 3n = 15 We will use division property here. 3n = 15 Subtract 2 to each side to get the variable on one side of the equal sign. 3n ÷ 3 = 15 ÷ 3 n = 5 Check: To check your solution substitute your answer in the given equation.

Copyright © Ed2Net Learning Inc. 15 Solve the equation: 4x/5 = 24 We will use both division & multiplication property here. 4x/5 = 24 Multiply 5 to each side (4x/5)×5 = 24×5 4x = 120 Now apply division property Divide by 4 to each side, we will get x = 30

Copyright © Ed2Net Learning Inc. 16 Solve the equation: 2c + c +12 = 78 2c + c +12 = 78 First combine the like terms, we will get 3c + 12 = 78 Subtract 12 from each side 3c = 78 – 12 3c = 66 Now apply division property Divide by 3 to each side, we will get c = 22

Copyright © Ed2Net Learning Inc. 17 Your Turn 1.X-3=5 Answer: X=8 2.X+5=8 Answer: X=3 3.X+3= 7-X Answer: X=5 4.2X + 8= 18 Answer: X=5 5.X- 1/3= 2/3 Answer: X=1 6. 5X+2= 22 Answer: X=4

Copyright © Ed2Net Learning Inc. 18 Your Turn 7. X*3=15 Answer: X=5 8. X*5=40 Answer: X=8 9. X/2= 6 Answer: X= X + 8= 18 Answer: X=5

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Copyright © Ed2Net Learning Inc. 20 Let us play a game Click here to play

Copyright © Ed2Net Learning Inc. 21 Q1. A parent measures his child height and finds it to be 100 mm. The kid is standing on a stool of height 50 mm. Last month when he had measured the height he had found it to be 145 mm. How much has the child grown in last one month. Write the equation for this model and solve it. Let the increase in height of the child be X mm. Then the equation will be X= After simplification we will get X= X= 5mm

Copyright © Ed2Net Learning Inc. 22 Q2. A gardener is planning a rectangular garden area in a community garden. His garden is next to a 10 m fence. The gardener has to make a fence of 42 m. What is the length of the fence? 10m Let x =length of a side adjacent to the fence Then x x = 42 So 2x + 10 = 42 Subtract 10 from each side 2x = x= 32 x=16m x x 10m

Copyright © Ed2Net Learning Inc. 23 Q3. Solve this equality with fractions 2x/3 + x/2 = 7 Solution 2/3(x) + 1/2 (x) = 7 Multiply both sides by 6 to remove the fractions 6* 2/3 * x + 6 * 1/2 * x = 7 * 6 After simplification, we will get 4x + 3x = 42 Now combine similar terms 7x= 42 X= 6 (by dividing each side by 70) Therefore the solution is x= 6

Copyright © Ed2Net Learning Inc. 24 Let Us Review Equation is an expression in which both the sides are equal A linear equation is an equation which has got one or two variables. The highest power any variable is one. A solution is that value of the unknown which satisfies the equation. Addition / subtraction or multiplication/ division property of equality can be used for finding the solution

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