In the equation y = kxz, what does y vary as?

In the equation y = kxz, where k is a constant, y is expressed as the product of x and z scaled by the constant k. This forms a relationship where y varies jointly with both x and z.

Joint variation means that y changes in proportion to the product of x and z. If either x or z increases, y will increase proportionally, provided the other variable remains constant. Similarly, if either x or z decreases, y will decrease proportionally.

Thus, the relationship laid out in the equation indicates that y is not only dependent on x or z individually, but on their combined effect, which supports the correct choice that y varies jointly as x and z.

This understanding of the joint variation provides clarity on how y responds to changes in both x and z, emphasizing the interconnectedness of these variables in the equation.