Patterns and Relationships

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Graphing Relations

A graph can also be used to show the relationship between two quantities

The relation is used to create an input/output table The data in the table is then graphed and when the

graphed points lie in a straight line, a linear relation is formed

Graphing Relations

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The relation 3n + 3 is used to create the table below and then the resulting data is graphed

Inputn

Output3n + 3

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1 6

2 9

3 12

4 15

5 18

6 21

Reading and Writing Equations

When one quantity equals another quantity an equation is formed.

Each quantity may be a number or an algebraic expression Every equation must have an equal sign(=) The variable in the equation represents an unknown

number, when that number is found the equation is solved

Examples of equations

2x – 1 = 212n = 104

Reading and Writing Equations

Ex. Write an equation for the sentence below

eight more than a number is 20

let n represent the numbereight more than n: 8 + nthe equation is : 8 + n = 20

Ex. Determine the equation for the following

John thinks of a number. He multiplies the number by 3, then adds 5.The answer is 23.

let n represent the numberthe number multiplied by 3: 3nthen adding 5: 3n + 5the equation is: 3n + 5 = 23

Solving Equations with Algebra Tiles

Algebra tiles a tiles or blocks that are used to visually represent an equation.

The tiles can be used to solve the equation There are two types of tiles Unit tiles are used to represent constants Variable tiles are use to represent the variable

Unit tile

Variable tile(x tile)

Solving Equations with Algebra Tiles

The expression 3x + 2 can be represented by

The equation 2x + 3 = 11 can be represented by

Solving Equations with Algebra Tiles

We can use tiles to solve equations. Draw a vertical line to represent the equal sign Place tiles on each side of the line to represent the

expression or number on each side of the equation. We want to get the x-tile by on its own, this is called

isolating the variable We then move or rearrange the tiles, keeping in

mind to always preserve the equality

Solving Equations with Algebra Tiles

Solve x + 3 = 11 by using algebra tiles

To isolate the x-tile remove 3 unit tiles from the left side and to preserve the equality do the same to the right side.

removeremove

Solving Equations with Algebra Tiles

The tiles show 1 x-tile equals 8 unit tiles so therefore the solution is x = 8