Final answer:
To find the equation of variation where y varies jointly as x and z, substitute the given values into the joint variation equation y = kxz to find the constant k. For y=324 when x=9 and z=9, the constant k is 4, resulting in the equation y = 4xz.
Step-by-step explanation:
When a student is told that y varies jointly as x and z, it means that the relationship between y, x, and z can be represented by the equation y = kxz, where k is the constant of variation. To find the equation of variation, we need to determine the value of k by using the given conditions. The student is provided with a situation where y equals 324 when both x and z are 9. By substituting these values into the joint variation formula, we get 324 = k(9)(9). From this, we can solve for k by dividing both sides by 81 (which is 9×9), resulting in k = 4.
The final equation of variation is y = 4xz. This means that for any values of x and z, y is four times the product of x and z.