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 in the equation y=7x is 7.
In this context, the constant of proportionality means that for every 1 road project (x), it takes 7 weeks (y) for the crew of workers to complete all the projects. This implies that the rate at which the number of road projects is completed is constant at 7 projects per week.
To find the constant of proportionality in the equation y = 7x, we can compare the given equation to the standard form of a proportionality equation, which is y = kx, where k represents the constant of proportionality.
Comparing both equations, we can see that the constant of proportionality in this case is 7. It 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 7.
In other words, it indicates that completing each road project takes approximately 7 weeks, assuming all projects have the same level of difficulty and require the same amount of time and effort from the crew of workers.
To find the constant of proportionality in the equation y = 7x, we need to look at the coefficient of x, which is 7 in this case. The constant of proportionality is the value that relates the dependent variable (y) to the independent variable (x) in a proportional relationship.
In this context, the constant of proportionality (7) means that for every unit increase in the number of road projects (x), it will take a crew of workers approximately 7 weeks (y) to complete all the projects. It indicates that the relationship between the number of road projects and the number of weeks needed to complete them is linear and consistent.
In simpler terms, it tells us that the crew of workers takes the same amount of time to complete each road project, and the time required is proportional to the number of projects they have to complete.