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
The constant of proportionality is 7.
In this context, the constant of proportionality means that for every unit increase in the number of road projects, the number of weeks it takes for the crew of workers to complete all the projects will increase by a factor of 7. This implies that the crew of workers takes an average of 7 weeks to complete each road project.
To find the constant of proportionality in the equation y = 7x, we need to compare the ratio of y to x for any given situation. In this case, the constant of proportionality is 7.
In the context of this equation, the constant of proportionality means that for every increase of 1 in the number of road projects (x), the number of weeks it takes to complete all the projects (y) will increase by a factor of 7. Similarly, if the number of road projects decreases by 1, the number of weeks needed to finish them will decrease by a factor of 7.
This essentially means that there is a direct linear relationship between the number of road projects and the time it takes to complete them. As the number of road projects increases, the time required for completion also increases proportionally.
The constant of proportionality is the number 7 in the equation y = 7x.
In this context, it means that for every additional road project (increasing x by 1), it would take a crew of workers approximately 7 more weeks (increasing y by 7) to complete all the projects. This implies that the crew's work rate is consistent, and they complete approximately one road project per week.