Your phone company charges $0.05 per minute for long distance phone calls on the weekend. Write a direct variation model that relates the total cost x to the number of minutes y spent talking on the phone.
y=0.05x ??
I don't know how to do this. Please help!!
You're wrong about one thing; you _do_ know how to do it. You just did it :-)
Yes, you are correct! The direct variation model that relates the total cost (x) to the number of minutes (y) spent talking on the phone can be represented as:
y = 0.05x
In this model, 'x' represents the total cost and 'y' represents the number of minutes. The constant of proportionality is 0.05, which is the charge per minute for long distance phone calls on the weekend.
Yes, you are on the right track! The direct variation model is indeed y = 0.05x, where y represents the number of minutes spent on the phone and x represents the total cost of the phone calls.
To understand how this model works, let's break it down:
- The number of minutes spent on the phone (y) and the total cost of the phone calls (x) are directly proportional. This means that as the number of minutes increases, the total cost also increases linearly.
- The constant of proportionality in this case is 0.05, which represents the cost per minute. This indicates that for each minute spent on the phone, the cost will be $0.05.
To apply this model, you can substitute the number of minutes spent on the phone (y) into the equation and solve for the total cost (x). For example, if you know that you talked for 50 minutes, you can substitute y = 50 into the equation and find the total cost:
y = 0.05x
50 = 0.05x
To solve for x, divide both sides of the equation by 0.05:
50 / 0.05 = x
x = 1000
So, if you talk for 50 minutes, the total cost of the phone calls would be $1000.
Remember, the direct variation model allows you to determine the relationship between the two variables and can help you calculate one variable when the other is known.