Identifying Linear Relationships and Functions

The video tutorial covers the concept of linear functions, focusing on the distinction between proportional and non-proportional relationships. It begins with an introduction to linear functions and their characteristics, followed by a detailed comparison of proportional and non-proportional relationships. The tutorial includes examples to illustrate these concepts, such as a rainfall scenario for proportional relationships and a temperature scenario for non-proportional relationships. The video aims to help students understand how to identify and differentiate these relationships using equations, tables, and graphs.

What is the primary goal of the lesson on graphing linear functions?

• To solve complex algebraic equations

• To learn about quadratic functions

• To complete a table and graph to determine if a function is linear

• To memorize equations

Which of the following is NOT a characteristic of a proportional relationship?

• The table includes the ordered pair (0, 0)

• The equation includes a constant term b

• The equation is in the form y = mx

• The graph passes through the origin

Which of the following is true about a linear relationship?

• It is always proportional

• It never passes through the origin

• It can be represented by a vertical line

• It is always a function except for vertical lines

How can you identify a non-proportional linear relationship from its equation?

• The graph passes through the origin

• The equation includes a constant term b

• The equation is in the form y = mx

• The table includes the ordered pair (0, 0)

What is the key difference between a proportional and a non-proportional linear relationship?

• The presence of a constant term b in the equation

• The slope of the line

• The color of the graph

• The number of points on the graph

In the rainfall example, what indicates that the relationship is proportional?

• The graph does not pass through the origin

• The equation includes a constant term b

• The graph is a curve

• The table includes the ordered pair (0, 0)

What is the rate of change in the rainfall example?

• 0.5 cm per hour

• 1.5 cm per hour

• 2.0 cm per hour

• 3.0 cm per hour

In the temperature example, why is the relationship not proportional?

• The graph passes through the origin

• The equation is in the form y = mx

• The equation includes a constant term b

• The table includes the ordered pair (0, 0)

What is the initial temperature at dawn in the temperature example?

• 5 degrees Fahrenheit

• 10 degrees Fahrenheit

• 12 degrees Fahrenheit

• 8 degrees Fahrenheit

In the context of the lesson, what does the term 'function' imply?

• A relationship that can be represented by any line

• A relationship that is always proportional

• A relationship that is always non-linear

• A relationship where each input has a unique output