Algebra 5.6 Standard Form. Different Forms of Linear Equations SI Form PS Form Vertical Line Horizontal Line Standard Form y = mx + b y – y 1 = m(x –

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Presentation transcript:

Algebra 5.6 Standard Form

Different Forms of Linear Equations 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

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

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

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 = -8 Then get all constants on the right x + y = -5

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 ] 4 Then clear the fraction y – 4 = 3x + 15 Next get x and y on the left. -3x -3x -3x + 4y – 4 = 15 Then get the constant on the right [-3x + 4y = 19] -1 Next get the coefficient of x positive. 3x - 4y = -19

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

You are buying food for a BBQ. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have $60. a) 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. xy x + 5y = 60 2(0) + 5y = 60 2x + 5(0) = 60 2(15) + 5y = 60 2(12) + 5y = 60 X lbs. Burgers y Chicken lbs (0, 20). (30, 0). (15, 10). (12, 12)

HW P (19-63 odd, 64-69)