Gregory teaches martial arts. He charges a one−time processing fee of $5.00 and the cost of the classes is shown below. Let x represent the number of classes and y represent the cost of classes. Based on this information, what will it cost to take 10 classes (including processing fee)?

Number of Classes, x: 1 2 3 4
Cost of Classes, y: $15 $27 $39 $51

Question

Gregory teaches martial arts. He charges a one−time processing fee of $5.00 and the cost of the classes is shown below. Let x represent the number of classes and y represent the cost of classes. Based on this information, what will it cost to take 10 classes (including processing fee)?

Number of Classes, x: 1     2     3     4     
Cost of Classes, y:    $15 $27 $39  $51

anonymous · Answer

The little diagram is the cost of classes not including the processing fee.

jim_thompson5910 · Answer

So the y values in the table do NOT include the processing fee of $5?

anonymous · Answer

Correct.

jim_thompson5910 · Answer

alright thanks

jim_thompson5910 · Answer

Notice how as x increases by 1, y increases by 12 

So the slope is 12/1 = 12 


This means that m = 12 


When x = 1, y = 15. 


Use this info in y = mx+b to find b 

y = mx+b 

15 = 12(1) + b 

15 = 12 + b 

15-12 = b 

3 = b 

b = 3 


So the equation that models the cost of x classes is y = 12x+3 


Now if you take 10 classes, then x = 10. Plug this in for x to find y 


y = 12x+3 

y = 12(10)+3 

y = 120+3 

y = 123 

So 10 classes will cost $123 (this is not counting the $5 processing fee) 


Add on the processing fee to get 123+5 = 128


So 10 classes will cost a total of $128

jim_thompson5910 · Answer

Sorry made a typo, but I fixed it

anonymous · Answer

Oh my gosh, thank you so much!

jim_thompson5910 · Answer

you're welcome