Answer:
[tex]z=-\frac{5xy}{96}[/tex]
Explanation:
We're told that z varies jointly with the product of x and y. This can be represented as;
[tex]\begin{gathered} z\propto xy \\ z=\text{kxy} \\ k=\frac{z}{xy} \end{gathered}[/tex]
We're also given the below values;
x = -4, y = 3, and z = 5/8
Let's go ahead and substitute these values into our equation and solve for k;
[tex]k=\frac{\frac{5}{8}}{-4\times3}=\frac{\frac{5}{8}}{-12}=\frac{5}{8}\times(-\frac{1}{12})=-\frac{5}{96}[/tex]
Since k = -5/96, the equation can now be written as;
[tex]z=-\frac{5xy}{96}[/tex]
