The business model for a company selling a service with no flat cost charges $3 per hour. What would the equation be as a proportional equation? If the company later decides to charge a flat rate of $10 for each transaction with the same per hour cost, what would be the new equation? How do these two equations compare when analyzed graphically? What is the same? What is different? Why?
The proportional equation for the company selling the service with no flat cost charges $3 per hour would be:
y = 3x
where y represents the total cost and x represents the number of hours.
When the company decides to charge a flat rate of $10 for each transaction with the same per hour cost, the new equation would be:
y = 10 + 3x
where y represents the total cost and x represents the number of hours.
When analyzed graphically, both equations represent a linear relationship with a positive slope. The only difference is the y-intercept, which is 0 in the first equation and 10 in the second equation.
Graphically, the same aspect is that both lines are straight and the slope remains the same, indicating a consistent per hour cost of $3. The difference lies in the initial cost of transactions, where the flat rate of $10 is added to the per hour cost in the second equation. This means that for small values of x (low hour values), the second equation will yield higher total costs compared to the first equation. However, as x increases, both lines will eventually have a similar slope and the difference in initial cost will be less significant.
In summary, the two equations have similar graphical characteristics, but differ in their initial cost added to the per hour charge.