The correct graph to show the relationship between the number of hours using the internet (x) and the cost (y) at a coffee shop, where it costs $2 per hour, is the first graph.
In this graph:
- The plotted points include (0, 0) which represents 0 hours and $0 cost.
- (1, 2) represents 1 hour and $2 cost.
- (2, 4) represents 2 hours and $4 cost.
This shows a linear relationship where the cost is proportional to the number of hours, specifically given by the function \( y = 2x \), where \( y \) is the cost and \( x \) is the number of hours. Therefore, the first graph accurately represents this relationship.