what is the equilibrim constant?plz explain?

let us have a equilibrium reaction as

X(g) +Y (g) → Z (g) (reversible sign cannot be shown so consider it urself.

for this reaction there exists a equilibrium constant K_eq
represented as

K_eq=[Z]/[X][Y]

whe [X],[Y],[Z] are concentrations of X Y Z respectively

here since it is equilibrium rate of forward reaction is directly proportional to the concentration of reactant and rate of backward reaction is directly proportional to concentration of prosucts

hence

rate of forward = k_f[X][Y]

where k_f is rate constant for forward reaction and

rate of backward = k_r [Z]

where k_r is rate constant for reverse reaction

but forward reaction=backward reaction

k_f[X][Y]=k_r[Z]

k_f/k_r = [Z]/[X][Y]

hence K_eq= [Z]/[X][Y]