Algebra 5. 6 Standard Form
Different Forms of Linear Equations n n n SI Form PS Form Vertical Line Horizontal Line Standard Form n n n 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 5 in Standard Form 5[y = 2 x – 3]5 First clear the fraction. n 5 y = 2 x -15 -2 x Then get x and y on the left side. n -1[-2 x + 5 y = -15] -1 Then get the coefficient of x positive. n 2 x - 5 y = 15 n 5
You try! Write -5 x + 11 = ½ y in Standard Form n 2 [-5 x + 11 = ½ y] 2 n -10 x + 22 = y +10 x Then get x and y on the same side. n 22 = 10 x + y Next rewrite with x and y on the left. n 10 x + y = 22 First clear the fraction.
We try! Write the standard form of an equation of the line passing through (-4, 3) with a slope of -2. n y – 3 = -2(x + 4) First write in PS form and distribute. n y – 3 = -2 x – 8 +2 x Then get x on the left. n 2 x + y – 3 = -8 +3 +3 Then get all constants on the right. n 2 x + y = -5
You try! Write the standard form of an equation of the line passing through (-5, 1) with a slope of ¾. n y – 1 = ¾ (x + 5) First write in PS form and distribute. n 4 [y – 1 = 3 x + 15 ] 4 Then clear the fraction. 4 n 4 4 y – 4 = 3 x + 15 -3 x n -3 x + 4 y – 4 = 15 +4 +4 -1 [-3 x + 4 y = 19] -1 n 3 x - 4 y = -19 n Next get x and y on the left. Then get the constant on the right. Next get the coefficient of x positive.
Write the standard form of the equation of… a) b) The horizontal line. Answer: y = 3 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 2 x + 5 y = 60 b) Model the possible combinations of each item you can buy with a table and a graph. y Chicken lbs. (0, 20) x y 2 x + 5 y = 60 . 0 20 30 0 2(0) + 5 y = 60 2 x + 5(0) = 60 15 10 2(15) + 5 y = 60 12 2(12) + 5 y = 60 12 10 5 . . (12, 12) (15, 10) 5 10 . (30, 0) X lbs. Burgers
HW n P. 311 -312 (19 -63 odd, 64 -69)
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