Final answer:
To determine the total cost of Joel's checking account over a period of time, the linear equation y = 4.95x is used, where y represents the total cost and x represents the number of months.
Step-by-step explanation:
The question involves creating a linear equation to represent the cost of having a checking account with a monthly service fee. Since Joel's bank charges him a monthly service fee of $4.95, the cost of maintaining his checking account is directly proportional to the number of months he has the account open.
To define the total cost of having the account, y, as a function of the number of months, x, we can use a linear equation in the form of y = mx + b, where m represents the slope (the rate of change) and b represents the y-intercept (the starting value when x is zero). In this case, there's no starting fee (y-intercept, b), so the equation simply becomes y = 4.95x. Here, the slope is $4.95, which represents the service fee charged each month.