SECTION 10.3GRAPHING LINEARRELATIONSHIPS
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I) WORKING WITH EQUATIONS
In this section you will be given an equation and thenasked to make a TOV with it
The equation will have two variables “x” and “y”
Variables are values that change (don’t stay the same)
For each “x” value you will have one corresponding “y” value
Together they become a coordinate [point] on a line
Suppose wemake “x”equal to 1
If “x” is equalto 1, then “y”will be equal to 7
The coordinateof the point willbe (1,7)
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II) GRAPHING LINEAR RELATIONS
Make a TOV
Plot the points on the grid
Connect the DOTS!!
Ex: Given the equation, make a TOV and graph it
x
y
0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
When making a TOV,
pick nice numbers for “x”
Plot the points on the grid
Connect the DOTS
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Practice: Make a TOV and graph the linear function
x
y
0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
When making a TOV,
pick nice numbers for “x”
Plot the points on the grid
Connect the DOTS
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III) WHAT IS A LINE MADE OF?
A line is actually made of many points(dots) that satisfy the equation.
If you zoom into a graph, you see a lotof tiny points that “line up” together
x
y
-1
0
1
2
3
-1
1
2
3
If keep zooming in, you get a lot more tinypoints that line up together
x
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
-0.4
-0.2
0.2
0.4
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So, a line is actually made up of billions of points (dots)
Every single point on the line will satisfy the equation!
IV) EQUATION OF A LINE PROPERTY
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EX: WHICH OF THE FOLLOWING POINTS WILL BE ONTHE LINE GIVEN BY THE EQUATION:
Since only the third point satisfies theequation, then the third point (3,3) will be onthe line
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V) EVALUATING EQUATIONS:
When you have an equation, you can solve for valuesby simply plugging in numbers
Ex: Given the following pattern, How many toothpickswill you need to make 87 triangles?
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