Create a graph showing the equations \(y=\frac13x\) and \(y=\frac13x-4\). Explain how the graphs are the same and how they are different.

An internet company charges \$70 per month for internet service to existing customers.

1. Write an equation representing the relationship between \(x\), the number of months of service, and \(y\), the total amount paid in dollars by an existing customer.
2. For new customers, there is a one-time \$100 installation fee. Write an equation representing the relationship between \(x\), the number of months of service, and \(y\), the total amount paid in dollars by a new customer.
3. Explain how graphs of the lines representing each situation would be the same and how they would be different.

A mountain road is 5 miles long and gains elevation at a constant rate. At the start of the road, the elevation is 4,800 feet above sea level. After 2 miles, the elevation is 5,500 feet above sea level.

1. Find the elevation of the road after 5 miles.
2. What is the vertical intercept and what does it represent in this situation?

Two angles are supplementary. One has a measurement that is twice as large as the other. Find the two angle measurements.