The relation between the slope of isothermal curve and slope of adiabatic curve

For isothermal Process, $PV =$ constant 

Differentiating both side

          $PdV+VdP=0$  or $\frac{dP}{dV}= \frac{P}{V}\times \gamma$

Again for adiabatic process, $P{V}^{\gamma } =$constant

Again differentiating both side

         $dP{V}^{\gamma }+\gamma V^{\gamma -1}dV P =0$ or $\frac{dP}{dV} = \frac{-P}{V} \times \gamma$

slope of adiabatic curve $= \gamma$ times slope of isothermal curve.