Proportional Relationships and Their Properties

This video tutorial covers the concept of proportional relationships, explaining that they must pass through the origin and form a straight line. It discusses the constant of proportionality, which is the slope or the ratio of rise over run. The tutorial also explains how to determine proportionality using tables and graphs, including calculating slope from a graph. Finally, it covers forming proportional equations and comparing different constants of proportionality to determine earnings per hour.

What are the two main criteria for a relationship to be considered proportional?

• It must be a straight line and pass through the origin.

• It must be a curved line and pass through the origin.

• It must be a straight line and pass through any point.

• It must be a curved line and pass through any point.

What is the term used to describe the constant steepness of a proportional relationship?

• Rate of change

• Variable slope

• Linear coefficient

• Constant of proportionality

How can you determine if a relationship is proportional using a table of values?

• By dividing each y-value by its corresponding x-value and checking for consistency

• By adding all the x-values and y-values together

• By checking if the y-values are all the same

• By checking if the x-values are all the same

In a table, what do the first and second columns typically represent?

• Y-values and X-values

• X-values and Y-values

• Outputs and Inputs

• Inputs and Outputs

If the ratio of y to x is consistent across a table, what does this indicate?

• The x-values are incorrect

• The y-values are incorrect

• The relationship is not proportional

• The relationship is proportional

What is the first step in finding the constant of proportionality from a graph?

• Calculate the area under the curve

• Find two points the line passes through

• Identify the x-intercept

• Identify the y-intercept

When drawing a slope triangle on a graph, what should you pay close attention to?

• The color of the graph

• The scale of the axes

• The thickness of the line

• The labels on the points

What does the slope of a line in a proportional relationship represent?

• The x-intercept

• The y-intercept

• The constant of proportionality

• The curvature of the line

What form does the equation of a proportional relationship take?

• y = kx

• y = kx + c

• y = mx + b

• y = x^2

Who had the highest earnings per hour in the given example?

• Sierra

• Betrix

• None of the above

• Avery