Indentifying Direct, Indirect, Proportional, and Inverse Relationships

Last class we had a very in depth conversation about the differences between these relationships. For each of them, we discovered a few unique traits that each must have.

1)      Direct

·        When x increases, so does y

Ø  This means the graph must have a positive slope. Whatever direction x moves, y must move in the same direction even if that means that they both move negatively.

·        Y-intercept

Ø  The graph can start anywhere on the y-axis.

·        Type of graph

Ø  Any type of education can represent a direct relationship as long as it follows the other traits.

2)      Indirect

·        “Not Direct”

Ø  Indirect literally breaks down into “not direct”. So whenever a graph does not follow all of the traits for direct it is indirect.

3)      Proportional

·    Δ x = Δ y   

Ø  In a proportional function, the change in x is equal to the change in y. So if x doubles, then y doubles also.

·        Y-intercept

Ø  In a proportional graph, the y-intercept must start at the origin. A y-intercept would not allow for the ratio between the change in x and y to remain proportional.

4)      Inverse

·        k/x (when k is a constant)

Ø  In this inverse parent function, it shows the opposite of proportional. If x doubles, y is cut in half.

*Also, some functions can be more than one of these relationships at the same time.