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 the projects, y. What is the constant of proportionality? What does it mean in this context?

1 answer

The equation \( y = 7x \) represents a linear relationship between the number of road projects \( x \) and the number of weeks \( y \) it takes to complete all the projects.

In this equation, the constant of proportionality is \( 7 \). This means that for every road project (each increment of \( x \) by 1), it takes an additional 7 weeks to complete all the projects.

In this context, the constant of proportionality \( 7 \) indicates that the time required to complete the road projects increases linearly with the number of projects. Specifically, if there are 1 project, it takes 7 weeks; if there are 2 projects, it takes 14 weeks, and so on. Thus, the crew needs 7 weeks for each additional project they undertake.