Question

The number of years, y, is a function of the number of months, m. The number of months, m, is also a function of the number of years, y. Write two equations, one to represent each function. Type the answers in the boxes below. Show that the number of months, m, is a function of the number of years, y: Show that the number of years, y, is a function of the number of months, m:

1) m=12y
2) y=m/12

Answer 1

One equation representing m in terms of y is m=12y. Another equation representing y in terms of m is y=m/12. The relationships between y and m can be demonstrated by substituting values into the equations.

Step-by-step explanation:

One equation representing the number of months, m, as a function of the number of years, y, is: m = 12y. This equation states that the number of months is equal to 12 times the number of years.

Another equation representing the number of years, y, as a function of the number of months, m, is: y = m/12. This equation states that the number of years is equal to the number of months divided by 12.

To show that the number of months, m, is a function of the number of years, y, we can substitute a value for y in the equation m = 12y and calculate the corresponding value of m. For example, if y = 2, then m = 12 * 2 = 24. Similarly, if y = 5, then m = 12 * 5 = 60. This shows that for every value of y, there is a unique value of m, which satisfies the definition of a function.