The equation, y = 7x, gives the relationship between the number of road projects, x, and the number of weeks it takes a crew of workers to complete all projects, y. What is the constant of proportionality? What does it mean in the context?

Question

The constant of proportionality is 7. It takes the crew of workers 7 days to complete 1 road project.
The constant of proportionality is 7. It takes the crew of workers 7 days to complete all of their road projects.
The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete 1 road project.
The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete all of their road projects.

Answer 1

The constant of proportionality in the equation \( y = 7x \) is indeed 7. This implies that for every 1 road project (x), it takes the crew of workers 7 weeks (y) to complete that project.

So, the correct statement in the context is: The constant of proportionality is 7. It takes the crew of workers 7 weeks to complete 1 road project.

This means that the crew takes a consistent duration of 7 weeks for each individual road project they work on, and the total time to complete multiple projects increases linearly based on the number of projects.