An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find and graph the number of devices, x, for which the cost of the new plan is less than the current plan.

Explanation:Here we know that an internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. Assuming just a month, we can write a constant equation given by the form:[tex]y=175 \\ \\ \\ Where: \\ \\ y:\text{Cost in dollars}[/tex]The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. So the linear equation is:[tex]y=94+4.5x \\ \\ \\ Where: \\ \\ x:\text{Number of months} \\ \\ y:\text{Number of devices}[/tex]So we need to find the number of devices, x, for which the cost of the new plan is less than the cost of the current plan. By using inequalities:[tex]94+4.5x<175 \\ \\ 4.5x<81 \\ \\ x<\frac{81}{4.5} \\ \\ x<18[/tex]So you should connect less than 18 devices in a month in order for the cost of the new plan to be less than the cost of the current plan.