SECTION 10.2 FINDING PATTERNSIN A TABLE OF VALUES
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I) WRITING EQUATIONS
We can use equations to model situations in the real world
Using equations, we can solve complex problems easily
The first step to writing equations is to find a pattern!
Ex: The following diagram shows the number of triangles createdwith a number of toothpicks used. Write an equation to describethe number of triangles (T) vs number of toothpicks (P).
The number of toothpicks used to equal to thenumber of triangles times “2” and then plus one
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x
y
3
5
7
9
11
13
15
17
1
2
3
4
5
6
7
Tooth Picks and Triangles
Number of Traingles
Number of Toothpicks
The values forma straight line,so it is a linearfunction
Practice: Tiles are placed around a rectangular garden asshown. Write an equation that shows the size of the gardenvs the number of tiles. Draw a graph to show whether if it’sa linear relationship
S-1
Size 2
Size 3
The number of tiles used to equal to thesize of the garden times “2” and thenplus six
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x
y
1
2
3
4
5
6
7
8
6
8
10
12
14
16
18
Yard Size and Number of Tiles
Number of Tiles
Yard Size
The values forma straight line,so it is a linearfunction
II) FINDING PATTERNS IN A TOV
Check if the rows are increasing at a consistent ratio
If one column is increasing faster, multiply the othercolumn by that constant
Compare the new column with the right column to derivean equation
Since the right column
is increasing TWICE asfast, multiply the leftcolumn by 2
Therefore, the equation will be:
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Practice: Find an equation for the following TOV’s
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IV) IS IT LINEAR??
There are two ways to check if a TOV is linear
1st: Is there a consistent ratio in the increase of the twocolumns?
If the increase of the two columns are in ratio, thenthe TOV is linear
2nd: The other method is to graph it out
If the coordinates form a straight line then it is linear
If the coordinates curve then it is non-linear
Practice: Given the TOV, check if they are linear by:
1. Checking the ratio
2. Graphing the coordinates
The values from each columnincrease at a different ratio.
Therefore, the TOV is non-linear
T
P
0
1
2
3
4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
From the graph, we can see that thedots don`t form a straight line