Characteristics of Linear Functions

The video tutorial introduces the concept of linear relations, focusing on the rate of change and initial value. It explores the differences between proportional and nonproportional linear relations, using examples of Grace and Kelly's travel scenarios. The tutorial examines linearity through graphs, tables, and equations, highlighting the characteristics of linear functions and their graphical representations. It also discusses the importance of a constant rate of change and how it is depicted in different mathematical representations.

What is a key characteristic of a linear relation?

• Non-linear graph

• Constant rate of change

• Variable rate of change

• No initial value

Which of the following is true about functions?

• All functions are linear

• Functions are a type of equation

• Functions cannot be graphed

• Functions always have a variable raised to the second power

What distinguishes a proportional linear relationship from a nonproportional one?

• Proportional relationships have a variable rate of change

• Nonproportional relationships have no initial value

• Proportional relationships pass through the origin

• Nonproportional relationships are not linear

In the context of the video, what is true about Grace's graph?

• It has a variable rate of change

• It is a straight line passing through the origin

• It is non-linear

• It does not pass through the origin

What is the defining feature of a linear graph?

• It has a constant rate of change

• It is a curved line

• It has multiple slopes

• It always passes through the origin

How can you identify a linear relationship in a table?

• The Y values change by a constant amount for each X increase

• The Y values change by different amounts

• The X values decrease

• The table has no pattern

What is a characteristic of a linear equation?

• It has a constant term only

• It has no variables

• It has variables raised to the second power

• It has variables raised to the first power

What does a nonproportional linear equation have that a proportional one does not?

• A constant of zero

• An initial value

• No variables

• A variable rate of change