Final answer:
To find the constant of variation and write an equation for the statement, we can use the formula for direct variation and solve for the constant. Using the given values of x, z, and y, we can find the value of the constant and write the equation. Finally, we substitute the new values of x and z into the equation to find the value of y.
Step-by-step explanation:
To find the constant of variation and write an equation for the statement, we need to use the formula for direct variation:
y = kx * z
where y is the dependent variable, x and z are the independent variables, and k is the constant of variation.
Given that when x = 4 and z = 2, y = 12, we can substitute these values into the equation and solve for k:
12 = k * 4 * 2
k = 12 / 8 = 1.5
Therefore, the equation for the relation is y = 1.5xz.
To find y when x = 6 and z = 3, we substitute these values into the equation:
y = 1.5 * 6 * 3 = 27
So, the answer is D) y = 24; y = 12.