# Equivalent Algebraic Equations - PowerPoint PPT Presentation

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## Equivalent Algebraic Equations

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### Equivalent Algebraic Equations Learn and use the distributive property Rewrite equations to determine whether they are equivalent Formalize algebraic properties – PowerPoint PPT presentation

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Title: Equivalent Algebraic Equations

1
Equivalent Algebraic Equations
• Learn and use the distributive property
• Rewrite equations to determine whether they are
equivalent
• Formalize algebraic properties
• Identify properties as they are used in solving
equations
• Introduce factoring as a reverse of the
distributive property

2
• In the previous lesson you learned to write the
equation of line using the point-slope form. You
were given the slope and a point.
• But remember that a line goes through many
points. Will the equation be equivalent if it
written using another point?
• In this lesson you will learn how to identify
different equations that describe the same line.

3
• If a line with slope 2 that passes through the
point (-4,3) can be described by the equation y
3 2(x4).
• This line also passes through (1, 13), so it can
also be described by the equation y132(x-1).

4
• If we place both of these equations in Y1 and Y2
in our graphing calculator, we see they produce
the same line when graphed.
• When a table is produced you can see that the
same set of values is produced.
• There are many equivalent equations that can be
used to describe a given line.

5
The Distributive Property
• Place the Distributive Property Template in your
Communicator.
• Lets picture 2(7) on grid paper.
• One way to describe its area is to say it is
2(43).
• Another way is to think of it as 2(4) 2(3), by
separating the rectangle into two parts.
• Notice that 2(7)2(43) 2(4)2(3)14
• This is called the distributive property.
• Model another distributive property on the grid
paper
• Write the distributive property on your
Communicator

6
The Distributive Property
• Place the Distributive Property Template in your
Communicator.
• Lets picture 2(x4) on the multiplication
rectangle.
• Place 2 units on the left. Place x 4 across
the top.
• Fill in the multiplication.
• We see that another way is to think of2(x4) is
2(x) 2(4).
• This is called the distributive property.
• Model another 3(x-1) on the multiplication
rectangle.
• Write the distributive property on your
Communicator

7
• We can use the distributive property to rewrite
some of our equations.
• Suppose y 3 2(x 4).
• Using the distributive property gives usy3
2(x) 2(4) or y 3 2x 8
• Or this can be rewritten as y 11 2x.
• Point Slope form y 3 2(x4)
• Slope Intercept form y 11 2x.
• Describe what each tells us.

8
Equivalent Equations
• Page 241

9
• Complete steps 1-5 with your group. Be prepared
to explain your thinking on each step.
1. y 3 - 2(x - 1)
2. y -5 - 2(x - 5)
3. y 9 - 2(x 2)
4. y 0 - 2(x - 2.5)
5. y 7 - 2(x 1)
6. y -9 - 2(x - 7)

10
• Complete steps 6-7 with your group.
1. y 2(x-2.5)
2. y182(x-8)
3. y52-6(x8)
4. y-62(x4)
5. y21-6(x4)
6. y-14-6(x-3)
7. y-102(x6)
• h. 6xy 4
• y112(x-8)
• 12x 2y-6
• y2(x-4)10
• y15-2(10-x)
• y72(x-6)
• y-6(x0.5)
• y-6(x2)16

11
Writing equation in different forms
• Intercept Form y a bx
• Point-Slope Form y y1 b(x - x1)
• An equation of the form ax by c are said to
be in standard form

12
Properties of Arithmetic
• Distributive Property
• Commutative Property of Multiplication
• Associative Property of Multiplication

13
Properties of Equality
• Given that a b, for any number c
• acbc Addition Property of Equality
• a-cb-c Subtraction Property of Equality
• acbc Multiplication Property of Equality
• a/c b/c (c?0) Division Property of Equality

14
Show two equations are equivalent
• y 2 3(x - 1)
• y 2 2x - 3
• y -1 3x
• Original Equation
• Distributive Property
• Combine Like Terms

So y 2 3(x - 1) is equivalent to the equation
y -1 3x.
15
Show two equations are equivalent
• 6x -2y 2
• -2y 2 - 6x
• y (2 - 6x)/-2
• y -1 3x
• Original Equation
• Subtraction Property
• Division Property
• Distributive Property

So 6x 2y 2 is equivalent to the equation y
-13x.
16
Checking for Equivalency
• You can enter the intercept form and the
point-slope form in the calculator to verify they
are equivalent.
• The Standard Form (ax by c) cannot be entered
in the calculator for verification.

17
• By using properties of equality solve the
equation
• Identify the properties you use on each step.