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Algebra

Algebra . 5.6 Standard Form. SI Form PS Form Vertical Line Horizontal Line Standard Form. y = mx + b y – y 1 = m(x – x 1 ) x = # y = # Ax + By = C -A and B are both not 0 -A and B are integers and A is positive. Different Forms of Linear Equations.

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Algebra

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  1. Algebra 5.6 Standard Form

  2. SI Form PS Form Vertical Line Horizontal Line Standard Form y = mx + b y – y1 = m(x – x1) x = # y = # Ax + By = C -A and B are both not 0 -A and B are integers and A is positive Different Forms of Linear Equations

  3. We try! Write y =2x – 3 in Standard Form5 • 5[y =2x – 3]5 First clear the fraction. 5 • 5y = 2x -15 Thenget x and y on the left side. -2x -2x • -1[-2x + 5y = -15] -1 Thenget the coefficient of x positive. • 2x - 5y = 15

  4. You try! Write -5x + 11 = ½ y in Standard Form • 2 [-5x + 11 = ½ y] 2First clear the fraction. • -10x + 22 = y Then get x and y on the same side. +10x +10x • 22 = 10x + yNext rewrite with x and y on the left. • 10x + y = 22

  5. We try! Write the standard form of an equation of the line passing through (-4, 3) with a slope of -2. • y – 3 = -2(x + 4)First write in PS form and distribute. • y – 3 = -2x – 8 Then get x on the left. +2x +2x • 2x + y – 3 = -8Then get all constants on the right. +3 +3 • 2x + y = -5

  6. You try! Write the standard form of an equation of the line passing through (-5, 1) with a slope of ¾ . • y – 1 = ¾ (x + 5)First write in PS form and distribute. • 4 [y – 1 = 3 x + 15 ] 4Then clear the fraction. 44 • 4y – 4 = 3x + 15Next get x and y on the left. -3x -3x • -3x + 4y – 4 = 15 Then get the constant on the right. +4 +4 • -1 [-3x + 4y = 19] -1 Next get the coefficient of x positive. • 3x - 4y = -19

  7. Write the standard form of the equation of… • The horizontal line. Answer: y = 3 • The vertical line. Answer: x = -3 . (2, 3) . (-3, -1)

  8. You are buying food for a BBQ. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have $60. • Write an equation that models different amounts of each item you can buy. Let x = lbs of hamburgers bought; Let y = lbs of chicken bought 2x + 5y = 60 b) Model the possible combinations of each item you can buy with a table and a graph. . (0, 20) y Chicken lbs. . (12, 12) x y . (15, 10) 2x + 5y = 60 10 5 . (30, 0) 0 20 2(0) + 5y = 60 30 0 2x + 5(0) = 60 5 10 X lbs. Burgers 15 10 2(15) + 5y = 60 12 12 2(12) + 5y = 60

  9. HW • P. 311-312 (19-63 odd, 64-69)

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