Algebra

5.6 Standard Form

Different Forms of Linear Equations

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

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.

+3 +3

2x + 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.

4 4

4y – 4 = 3x + 15 Next 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

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.x y

200

030

15 10

12 12

2x + 5y = 60

2(0) + 5y = 60

2x + 5(0) = 60

2(15) + 5y = 60

2(12) + 5y = 60

X lbs.Burgers

y Chicken lbs.

5 10

10 5

. (0, 20)

. (30, 0)

. (15, 10). (12, 12)

HW

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