The equation y = 7x gives the relationship between the number of road projects, x, and the number of weeks it takes the crew of workers to complete all the projects, y. What is the constant of proportionality? What does it mean in this context
The constant of proportionality in this context is the number 7. It means that for every road project completed, it takes the crew of workers 7 weeks to finish it.
To find the constant of proportionality in the equation y = 7x, you can observe that the equation is in the form of y = kx, where k is the constant of proportionality. In this case, k = 7.
In the context of the equation, the constant of proportionality represents the rate at which the number of road projects, x, is related to the number of weeks it takes to complete them, y. It indicates that for every increase of one road project, the crew of workers takes 7 weeks to complete all the projects. It implies that completing each road project requires approximately 7 weeks of work by the crew.
To find the constant of proportionality in the equation y = 7x, we can observe that y is directly proportional to x. Therefore, the constant of proportionality is the coefficient of x, which is 7.
In this context, the constant of proportionality of 7 means that for every 1 unit increase in the number of road projects (x), it will take the crew of workers approximately 7 weeks (y) to complete all the projects. This means that the crew's productivity or efficiency is such that they can complete 7 road projects in 1 week.