Algebra 5.6 Standard Form. Different Forms of Linear Equations SI Form PS Form Vertical Line...
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Transcript of Algebra 5.6 Standard Form. Different Forms of Linear Equations SI Form PS Form Vertical Line...
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)