Final answer:
The linear equation representing the hours Yuson has left for community service after x days is y = 30 - 2x, with y being the hours remaining and x the days spent doing community service.
Step-by-step explanation:
To represent the hours Yuson has left of community service after x days, we need to establish a linear equation. Yuson must complete a total of 30 hours of community service and does 2 hours each day. Therefore, after each day, the amount of service remaining decreases by 2 hours.
Let y represent the hours of community service left after x days. Initially, Yuson has 30 hours remaining, so when x is 0, y is 30. Each day decreases the total by 2 hours, thus the slope of our equation (which represents the rate of completing the service) is -2.
Our linear equation is y = 30 - 2x.
This equation shows that for every day x that Yuson does community service, the total hours left, y, is reduced by 2 from the starting point of 30 hours.