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6-8 Standard Form for the Equation of a Line

6-8 Standard Form for the Equation of a Line. Big Idea Every line has an equation of the form Ax + By = C. Goal Write an equation for a line in standard form. Graph 5 x + 2 y = 10. 5 x + 2 y = 10 5(0) + 2y = 10 2y = 10 y = 5 (0, 5)

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6-8 Standard Form for the Equation of a Line

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  1. 6-8 Standard Form for the Equation of a Line Big Idea Every line has an equation of the form Ax + By = C. Goal Write an equation for a line in standard form.

  2. Graph 5x + 2y = 10. • 5x + 2y = 10 • 5(0) + 2y = 10 • 2y = 10 • y = 5 • (0, 5) • 5x + 2y = 10 • 5x + 2(0) = 10 • 5x = 10 • x = 2 • (2, 0) 7 6 5 4 3 2 1 1 2 3 4 5

  3. ( )5 _ 31 5 5 2. Rewrite y = x - in standard form with integer coefficients. Tell the values of A, B, and C. y = x- _ 31 5 5 5y = -3x – 1 +3x +3x 3x + 5y = -1 A = 3, B = 5, C = -1 y = -0.8x ( )10 10y = - 8x +8x +8x 8x + 10y = 0 3. Rewrite y = −0.8x in standard from with integer values of A, B, & C.

  4. Rewriting Equations in Slope-Intercept and Standard Form Equation Slope-Intercept Form Standard Form 1. 20x - 5y = 35 2. y - 5 = 8(x - 1) 3. 2x + 4(y + x) = 5y + 15 4. y = x + 11 5. 14x + 4y = 20 y = mx + b Ax + By = C y = 4x – 7 4x – y = 7 y = 8x – 3 8x – y = 3 y = 6x – 15 6x - y = 15 y = x + 11 2x - 3y = -33 y = x + 5 7x + 2y = 10 2 3 2 3 _7 2 2. y – 5 = 8(x – 1) y – 5 = 8x – 8 y = 8x – 3 -8x -8x -8x + y = -3 • 20x - 5y = 35 • 20x – 5y = 35 • 4x – y = 7 ( ) / 5 -4x -4x - y = -4x + 7 -1( ) 8x – y = 3 -1( ) y = 4x - 7

  5. 2 3 3. 2x + 4(y + x) = 5y + 15 4. y = x + 11 2x + 4y + 4x = 5y + 15 6x + 4y = 5y + 15 -5y -5y 6x - y = 15 -6x -6x - y = -6x + 15 2 3 y = x + 11 3( ) 3y = 2x + 33 -2x -2x -2x + 3y = 33 -1( ) 2x - 3y = -33 -1( ) y = 6x – 15 ( ) / 2 7x + 2y = 10 5. 14x + 4y = 20 -7x -7x 2y = -7x + 10 ( ) / 2 y = x + 5 _7 2

  6. Lourdes spent $24 on 30 neon bouncing balls and 12 glow-in-the-dark necklaces. Write an equation in standard form then answer the questions below. 1. If a neon ball cost $0.30, then how much did a necklace cost? 2. What is the most a necklace could have cost? What is the cost of one neon ball? 3. What is the most a neon ball could have cost? #neon balls  price of 1 ball + #necklaces  price of 1 necklace = total 30x + 12y = 24 1. 30x + 12y = 24 30(.30) + 12y = 24 9 + 12y = 24 12y = 15 y = 1.25 a necklace costs $1.25 2. Max when 0 neon balls 30(0) + 12y = 24 12y = 24 y = 2 Max price of a necklace $2.00 Neon ball is free. 3. Max when 0 necklaces 30x + 12(0) = 24 30x = 24 x = .8 Max price of a neon ball $.80

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