Exploring Linear Functions through Graphing

The video tutorial covers the concept of linear functions, focusing on proportional and non-proportional relationships. It explains how to identify these relationships using equations, graphs, and tables. The tutorial provides examples to illustrate both proportional and non-proportional relationships, emphasizing the importance of the y-intercept in determining proportionality. The video also discusses the vertical line test to determine if a relationship is a function.

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

• To understand quadratic functions

• To use an equation to complete a table and graph to determine if the function is linear

• To learn about exponential functions

• To study the properties of circles

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

• A table that includes the ordered pair (0, 0) and has a constant rate of change

• An equation in the form y = mx + b

• An equation in the form y = mx

• A graph that is a line passing through the origin

What is the only type of line that is not a function?

• Curved line

• Horizontal line

• Diagonal line

• Vertical line

Which term is the most specific when describing relationships?

• Linear

• Proportional

• Function

• Relationship

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

• The slope of the line

• The presence of a y-intercept (b) in the equation

• The x-intercept of the line

• The color of the graph

In a proportional relationship, what is the value of the y-intercept (b)?

• It varies

• 1

• 0

• It is undefined

How can you verify that a relationship is proportional using a graph?

• The graph is a horizontal line

• The graph is a curve

• The graph passes through the origin and is a straight line

• The graph has multiple lines

What is the rate of change in the rainfall example?

• 2.0

• 3.0

• 0.5

• 1.5

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

• Because the slope is negative

• Because the equation includes a y-intercept (b) of 8

• Because the graph is a curve

• Because the table values are incorrect

What is the equation representing the temperature example?

• y = 2x + 8

• y = 2x

• y = 8x + 2

• y = x + 2