Understanding Proportional Relationships

The video tutorial by Mr. Moraga covers proportional relationships and graphs. It explains the concept of the constant of proportionality, using examples like showerhead water usage and house cleaning costs. The tutorial demonstrates how to identify proportional relationships through tables and graphs, and how to write equations for these relationships. It also contrasts proportional and non-proportional relationships using examples like bowling costs. The video concludes with a summary of key points and emphasizes the importance of understanding unit rates and graphing techniques.

What is the equation used to represent proportional relationships?

• y = mx + b

• y = kx

• y = x + c

• y = ax^2 + bx + c

In the showerhead example, what does the constant of proportionality (k) represent?

• The total gallons used

• The time taken for a shower

• The number of gallons per minute

• The number of minutes

What is the unit rate in the showerhead example?

• 5 gallons per minute

• 20 gallons per minute

• 10 gallons per minute

• 15 gallons per minute

How can you determine if a graph represents a proportional relationship?

• The graph has a negative slope

• The graph has a positive slope

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

• The graph is a curve

What does the constant of proportionality indicate in a graph?

• The curvature of the graph

• The y-intercept of the graph

• The slope of the graph

• The x-intercept of the graph

What is the significance of the origin in a proportional relationship graph?

• It indicates the maximum value

• It shows the starting point of the graph

• It confirms the relationship is proportional

• It represents the average value

In the house cleaning company example, what does the point (1, 45) on the graph represent?

• 45 hours of work

• 1 hour of work costing $45

• 45 minutes of work

• 1 minute of work costing $45

Why is the bowling example not considered a proportional relationship?

• The graph is a straight line

• The cost decreases over time

• The graph does not pass through the origin

• The cost increases linearly

In the bicyclist example, what does the point (1, 15) represent?

• 1 hour in 15 miles

• 1 mile in 15 minutes

• 15 miles in 1 hour

• 15 minutes in 1 mile

How do you calculate the constant of proportionality from a graph?

• Subtract the x-coordinate from the y-coordinate

• Divide the y-coordinate by the x-coordinate

• Add the x-coordinate to the y-coordinate

• Multiply the x-coordinate by the y-coordinate