Characteristics and Representations of Linear Functions

The video tutorial explains how to identify linear functions using tables, graphs, and equations. It begins by defining a linear function as one with a constant rate of change. The tutorial then examines a table, confirming its linearity by showing a consistent addition of 3. Next, it analyzes a graph, identifying it as non-linear due to a changing slope, indicating an exponential function. Finally, the video evaluates an equation in the form y = mx + b, confirming its linearity with a constant slope of 7. The tutorial concludes that the table and equation represent linear functions, while the graph does not.

What is a key characteristic of a linear function?

• It has a variable rate of change.

• It always increases.

• It has a constant rate of change.

• It always decreases.

In the table, what is the rate of change between consecutive values of F(x)?

• Add 2

• Multiply by 3

• Add 3

• Subtract 3

Why is the table considered to represent a linear function?

• Because it has a decreasing rate of change.

• Because it shows exponential growth.

• Because it has a constant rate of change.

• Because it has a variable rate of change.

What indicates that the graph does not represent a linear function?

• The graph is horizontal.

• The graph is a straight line.

• The slope changes at different points.

• The slope is constant throughout.

What type of function does the graph represent?

• Constant function

• Exponential function

• Linear function

• Quadratic function

What is the standard form of a linear equation?

• y = mx + b

• y = a^x

• y = ax^2 + bx + c

• y = x^2 + bx + c

In the equation s = 7D + 2, what does the number 7 represent?

• The y-intercept

• The slope

• The constant term

• The variable

Why is the equation s = 7D + 2 considered linear?

• Because it is in the form y = mx + b.

• Because it has a variable slope.

• Because it represents exponential growth.

• Because it has no intercept.

Which representations were identified as linear in the conclusion?

• The graph and the equation

• The table and the equation

• Only the graph

• Only the table

What is the role of the y-intercept in a linear equation?

• It makes the function exponential.

• It is the starting value of the function.

• It determines the slope.

• It changes the rate of change.