Transcript 7math-unit1-s6-9

Patterns and Relationships
Graphing Relations
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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
The relation 3n + 3 is used to create the table
below and then the resulting data is graphed
Input
n
Output
3n + 3
0
3
1
6
2
9
3
12
4
15
5
18
6
21
Reading and Writing Equations
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When one quantity equals another quantity an equation is
formed.
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Each quantity may be a number or an algebraic expression
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Every equation must have an equal sign(=)
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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
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
Solving Equations with Algebra Tiles
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Algebra tiles a tiles or blocks that are used to visually
represent an equation.
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The tiles can be used to solve the equation
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There are two types of tiles
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Unit tiles are used to represent constants
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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
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We can use tiles to solve equations.
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Draw a vertical line to represent the equal sign
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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.
remove
remove
Solving Equations with Algebra Tiles
The tiles show 1 x-tile equals 8 unit tiles so therefore the solution is x = 8