Understanding Proportional Relationships

The video tutorial covers proportional relationships using tables, equations, and graphs. It begins with an introduction to the topic, followed by an activity where students graph points and complete tables. The concept of constant proportionality is explored, and students learn to write equations for proportional relationships. The tutorial includes a real-world example of a hot dog eating contest to illustrate these concepts. Finally, homework problems are provided to reinforce learning.

What are the three main tools used to explore proportional relationships in this lesson?

• Graphs, diagrams, and tables

• Equations, charts, and models

• Tables, charts, and diagrams

• Tables, equations, and graphs

How do you determine the constant of proportionality from a table of values?

• By multiplying the x and y values

• By subtracting the x value from the y value

• By dividing the y value by the x value

• By adding the x and y values

Which of the following is a correct equation for a proportional relationship?

• y = x - k

• y = k + x

• y = kx

• y = x/k

What does a steeper line on a graph indicate about the slope?

• The slope is smaller

• The slope is larger

• The slope is zero

• The slope is negative

If a line passes through the origin, what does it indicate about the relationship?

• It is a proportional relationship

• It is an inverse relationship

• It is a quadratic relationship

• It is a non-linear relationship

In the hot dog eating contest example, what does the constant of proportionality represent?

• The number of hot dogs eaten per minute

• The total number of hot dogs eaten

• The time taken to eat one hot dog

• The number of minutes per hot dog

What is the effect of choosing a different independent variable on a graph?

• It changes the shape of the graph

• It changes the color of the graph

• It changes the direction of the graph

• It changes the scale of the graph

How can you describe the relationship between time and volume in the leaky faucet example?

• Time and volume have a constant rate of change

• Time and volume are inversely proportional

• Volume is independent of time

• Time is dependent on volume

What is the unit rate of honey cost per ounce if 12 oz costs $5.40?

• $0.50 per ounce

• $0.60 per ounce

• $0.45 per ounce

• $0.55 per ounce

In the trail mix example, what is the ratio of peanuts to raisins for a proportionality greater than one?

• 5:4

• 3:2

• 2:3

• 4:5