Suppose that z is inversely proportional to y and that z=12 when y=16. Write an equation that expresses z in terms of y.
4*(z)=1/4*(y)
It would be y=1/z so 16=1/12 or 1/(4*z)=4*y
Ignore the previous answers
z = C/y
Use the known data point to solve for C
12 = C/16
C = 192
Therefore
z = 192/y
To write the equation that expresses z in terms of y, we need to understand what it means for z and y to be inversely proportional. Inverse proportionality means that as one variable increases, the other variable decreases at a constant rate. Mathematically, we can express inverse proportionality as:
z = k/y
where k is the constant of proportionality.
To find the value of k, we can use the given information that z = 12 when y = 16. Substituting these values into the equation, we get:
12 = k/16
To solve for k, we can multiply both sides of the equation by 16:
12 * 16 = k
k = 192
Now that we have the value of k, we can substitute it back into the equation to get the final equation that expresses z in terms of y:
z = 192/y