Final answer:
Using the straight line depreciation equation, y = -2,150x + 17,200, by setting y to zero and solving for x, we find that it will take 8 years for the motorcycle to completely depreciate in value.
Step-by-step explanation:
The student has asked about the time it will take for a motorcycle to completely depreciate in value using the straight line depreciation equation y = -2,150x + 17,200. To find the number of years, we need to determine when the value of y (the value of the motorcycle) will reach zero. Setting the equation equal to zero and solving for x will give us the total depreciation time:
0 = -2,150x + 17,200
Add 2,150x to both sides:
2,150x = 17,200
Now divide both sides by 2,150 to solve for x:
x = 17,200 / 2,150
x = 8
Therefore, it will take 8 years for the motorcycle to totally depreciate.