Final answer:
A linear equation representing the total monthly cost of a plan is written as y = mx + b, where y is the total cost, x is the number of months, m is the monthly rate, and b is the initial fee or discount. Examples are provided with a monthly cost and varying initial fees or discounts.
Step-by-step explanation:
To write a linear equation representing the total monthly cost of a plan, where y is the total monthly cost and x is the number of months, we should follow a structure similar to the slope-intercept form (y = mx + b) or the point-slope form. In both forms, m stands for the slope, which represents the rate of change, and b stands for the y-intercept, which is the starting value when x equals zero.
For instance, let's say the plan has a monthly cost of $100 and a one-time signup fee of $50. The equation would then be written as y = 100x + 50, where 100 is the slope, representing the cost per month, and 50 is the y-intercept, representing the initial signup fee.
Another example could be a plan with a monthly rate of $30 and no initial fees, which can be expressed as y = 30x. In this case, the slope is 30, and since there are no initial fees, the y-intercept b is 0.
If the plan has an initial discount or credit, that amount would be subtracted from the total cost equation. For example, if there is a $20 initial discount, the equation would be y = 100x - 20.