<s>[INST] I am a high school student, and every year on my birthday, my parent usually gives me a watch as a gift. When I turned 12, I received a Casio watch, and since then, for every year I turn a year older, the amount they spend on my gift watches have increased by $10. The watch I received on my 12th birthday cost them $62.

Now, on my 18th birthday, I received a watch that costs $122. Since this time, I have not gotten any more watches. I know you can help me figure out if my parents are guilty of inconsistency on gifts or if they've been consistent all along.

Determine if my parents are consistent with their gift-giving by designing a mathematical model of the cost of the watch each year based on how much older I am than 12. Let y be the cost of the watch and let x be my age minus 12. Write the linear equation in slope-intercept form to model this situation. Then, determine the y-intercept (the cost of the watch I received when I first started receiving watches on my 12th birthday) directly from the problem statement as well as from the equation and see if they match.

First, take note of the information provided by the problem:

- The watch I received on my 12th birthday cost them $62. 
- For every year I turn a year older, the amount they spend on my gift watches have increased by $10.
- The watch I received on my 18th birthday cost them $122.

Let's start by calculating the slope of the line.
Given that it costs $10 more each year, we can say the slope, m, is equal to 10.

What do I do next?[/INST]