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