To solve this problem, we need to first create equations representing the cost of each plan, then calculate and compare the cost for each plan given that there are 6 dogs.
The Power Paws plan charges $3.00 per week, plus an additional 50 cents for each dog. This can be represented using the linear equation Ypp = 3 + 0.5X, where X represents the number of dogs and Ypp represents the cost of the Power Paws plan.
The Daring Doggies plan charges $4.00 per week, plus an additional 40 cents for each dog. This can be represented using the linear equation Ydd = 4 + 0.4X, where X again represents the number of dogs and Ydd represents the cost of the Daring Doggies plan.
Now we can substitute X = 6 (the number of dogs) into both equations to find out how much each plan would cost:
For the Power Paws plan, we find Ypp = 3 + 0.5*6 = $6.00.
For the Daring Doggies plan, we find Ydd = 4 + 0.4*6 = $6.40.
Therefore, the Power Paws plan would be cheaper for 6 dogs, costing $6.00 per week compared to $6.40 per week for the Daring Doggies plan.
To graph the solution, we can plot both equations on the same graph with the number of dogs (X) along the horizontal axis and the cost (Ypp and Ydd) along the vertical axis. The point of intersection would indicate the number of dogs for which both plans cost the same. For a number of dogs less than this, Power Paws will be cheaper, and for a number of dogs greater than this, Daring Doggies will be cheaper. However, since we are only interested in the cost for 6 dogs, and we have already solved this, visual graphing is not necessary for this particular problem.