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PPT – Equivalent Algebraic Equations PowerPoint presentation | free to download - id: 78e425-YThiZ

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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

- 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.

- 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).

- 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.

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

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

- 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.

Equivalent Equations

- Page 241

- Complete steps 1-5 with your group. Be prepared

to explain your thinking on each step.

- y 3 - 2(x - 1)
- y -5 - 2(x - 5)
- y 9 - 2(x 2)
- y 0 - 2(x - 2.5)
- y 7 - 2(x 1)
- y -9 - 2(x - 7)

- Complete steps 6-7 with your group.

- y 2(x-2.5)
- y182(x-8)
- y52-6(x8)
- y-62(x4)
- y21-6(x4)
- y-14-6(x-3)
- 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

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

Properties of Arithmetic

- Distributive Property
- Commutative Property of Addition
- Commutative Property of Multiplication
- Associative Property of Addition
- Associative Property of Multiplication

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

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.

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.

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.

- By using properties of equality solve the

equation - Identify the properties you use on each step.