7) The equation that relates the variables is z = (1/12)xy.
8) The equation that relates the variables is z = -3/40xy.
How the equation of that relates variables is derived
7)Given that
z varies jointly with the product of x and y
z ∝ xy
z = kxy
k = z/xy
if x = 3, y = 8 and z = 2
then the constant of proportionality is
k = 2/3 * 8
k = 1/12
Therefore, the equation that relates the variables is z = (1/12)xy.
8) Given that
z ∝ xy
z = kxy
k = z/xy
if x = -5, y = 2 and z = 3/4
then,
k = 3/4 / (-5) 2
k = 3/-40 = -3/40
substitute into z = kxy
z = -3/40xy.
Therefore, the equation that relates the variables is z = -3/40xy.