1. Patterns and Relationships

2. 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

3. Graphing Relations The relation 3n + 3 is used to create the table below and then the resulting data is graphed Input n Output 3n + 3 03 16 29 312 415 518 621

4. 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 = 21 2n = 104

5. Reading and Writing Equations Ex. Write an equation for the sentence below eight more than a number is 20 let n represent the number eight more than n: 8 + n the 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 number the number multiplied by 3: 3n then adding 5: 3n + 5 the equation is: 3n + 5 = 23

6. 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)

7. Solving Equations with Algebra Tiles The expression 3x + 2 can be represented by The equation 2x + 3 = 11 can be represented by

8. 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

9. 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. remove

10. Solving Equations with Algebra Tiles The tiles show 1 x-tile equals 8 unit tiles so therefore the solution is x = 8