how is the slope of an adiabatic curve steeper than an isothermal curve ?

For an adiabatic process we have

PV^γ = constant

so, by differentiating

(dP/dV)_A = -γPV^γ-1 / V^γ

so, slope of adiabatic process

(dP/dV)_A =  -γ(P/V)

For isothermal process,

(dP/dV)_I = -(P/V)

Thus, the slope of an adiabatic curve is γ times greater than the slope of an isothermal curve.