Linear Functions Introduction
We model many relationships between quantities as a linear function or straight line.
Even if the relationship between two quantities is not a straight line, a straight line is a good model that allows good predictions in a small area. For example, the earth is round but using a flat model is useful for building things.
In a linear model for a given change anywhere in the independent
variable (x-axis) there is the same change in the independent
variable.
This is equivalent to saying the slope is the same anywhere in the
relationship.
Linear relationships are defined by a straight line when graphed and allow easy prediction.
Implications of Linear Relationships
- What sorts of questions can you answer with a linear function?
- What is the significance of a change in the slope?
- Can part of a graph be linear and others not?
Concepts
- Association/Correlation
- Independent variable
- Dependent variable
- Slope
- Proportional Relationship
Association/Correlation
- Two variables are correlated when the change in one variable results in a predictable change in the other variable.
Independent Variable
- The variable we can manipulate
- The variable we want to see the effect of changing
- Placed on the x-axis
Dependent Variable
- The variable we observe when we manipulate the independent variable
- Placed on the y-axis
Slope
This quantity relates a change in the independent variable to the change in the dependent variable.