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Linear Relationships

A relation is one way to show a relationship between variables or sets of data. Graphing relations is a way of using pictures to represent relationships between two quantities. A line graph is a type of relation that can be classified as one of the following:

• a straight line
• a curved line
• no relationship

A graph is considered to be linear if and only if the points form a straight line.


The graph below is a non-linear relation since the graph does not consist of a straight line.


Non- Linear Relation: Curved line 

If the points seem to be scattered everywhere without any connection, then it is not a relation.

Points without a pattern (no correlation)

 

Example 1

Label the following graphs as a linear relation, a non-linear relation, or not a relation.

a.

Solution

Graph a is a non-linear relation because the line drawn is not straight, but a general trend can be seen.

b.

Solution

Graph b is a linear relation because the line drawn is straight, and a general trend can be seen.

c.

Solution

Graph c is a not a relation since the points plotted do not appear to have any relationship with each other.

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