There is a proportional relationship between the volume of a sample of helium in liters and the mass of that sample in grams. If the mass of a sample is 5 grams, its volume is 28 liters. \((5, 28)\) is shown on the graph below.

1. What is the constant of proportionality in this relationship?
2. In this situation, what is the meaning of the number you found in part a?
3. Plot at least three more points on the graph, and label with their coordinates.
4. Write an equation that shows the relationship between the mass of a sample of helium, in grams, and its volume, in liters. Use \(m\) for mass and \(v\) for volume.

Explain how the parts of the balanced hanger diagram compare to the parts of the equation.

\(7=2x+3\)

For the hanger diagram shown:

1. Write an equation with the variable \(x\) to represent the relationship.
2. Draw more hanger diagrams or describe how you would change the given diagram to show each step you would take to find the value of \(x\). Explain your reasoning.
3. Write an equation to represent each hanger diagram you drew or each change you would make to the given diagram. Explain how each equation matches its diagram.