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Look at the graph. What type of relationship does the shape of the graph illustrate? We must represent this curvature in the scale of the horizontal axis. So we need to do some mathematics to manipulate the values on the horizontal axis to eliminate the curvature.(If you see a power relationship, eg, y = x2, square the x values and plot y vs. x2)Now your graph should be linear, and you can find a slope.
Graphical Analysis
Developing Relationships
Why Do Linear Relationships Help?
Linear Relationships are useful because they provide an easily interpretable syntax. It also helps that we are comfortable working with them.
How Do We Write Linear Relationships?
Which Non-linear Relationships Are Common?
Linear Relationship: yx
Powers: yxn, n>1
Root relationship: yx
Inverse: yx-n, n>1
How Do We Work With Non-linear Relationships?
Worked Example
Independent Variable
Dependent Variable
Time (s)
Position (m)
0.0
0.1
1.0
2.0
2.0
8.0
3.0
18.0
4.0
32.0
5.0
50.0
There are no rows in this table
Independent Variable
Dependent Variable
Time (s)
Time² (s²)
Position (m)
0.0
0.0
0.1
1.0
1.0
2.0
2.0
4.0
8.0
3.0
9.0
18.0
4.0
16.0
32.0
5.0
25.0
50.0
There are no rows in this table
Practice
0
0
2
25
4
102
6
224
8
401
There are no rows in this table
0
0
1
0.33
2
1.32
3
2.97
4
5.28
There are no rows in this table
0
0
3
1.3
5
1.68
7
1.98
12
2.6
There are no rows in this table
2
37.5
6
12.5
10
7.5
17
4.41
There are no rows in this table
8
1.54
12
1.02
17
0.72
30
0.41
There are no rows in this table
3
11.6
10
21.1
28
35.3
51
47.6
There are no rows in this table
0.5
53.3
1.5
30.2
2.5
23.4
5.5
15.8
There are no rows in this table
3
4.11
11
0.31
15
0.16
35
0.03
There are no rows in this table
7
102
19
62
31
49
42
42
There are no rows in this table
Interpreting Slopes of Graphs
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