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 proportionally? what does it mean in this context?
The constant of proportionality in this equation is 7.
In this context, it means that for every increase of 1 project (x), the number of weeks (y) required to complete all the projects will increase by a factor of 7. This implies that the crew of workers takes 7 weeks to complete one road project.
In the equation y = 7x, the constant of proportionality is 7.
In this context, the constant of proportionality (7) represents the rate at which the crew of workers completes the road projects. It means that for every increase of one road project (x), it will take approximately 7 weeks (y) for the crew to complete all the projects.
To find the constant of proportionality in the equation y = 7x, we can observe that the coefficient of x, which is 7, represents the constant of proportionality.
In this context, the constant of proportionality (7) represents the rate at which the number of road projects (x) and the number of weeks it takes to complete them (y) are related. Specifically, it tells us that for every unit increase in the number of road projects, it takes 7 units of time (weeks) to complete them.
In other words, if we were to double the number of road projects from x to 2x, it would take 7 times as many weeks to complete all the projects (from y to 14y). Similarly, if we were to halve the number of road projects from x to 0.5x, it would also halve the number of weeks required for completion (from y to 0.5y).
So, the constant of proportionality acts as a conversion factor that helps us determine the relationship between the number of road projects and the time required to complete them.