Therefore,31​=∣∣​1+m(2m)2m−m​∣∣​31​=∣∣​1+2m2m​∣∣​31​=1+2m2m​​ 31​=∣∣​1+m(2m)m−2m​∣∣​ 31​=∣∣​1+2m2−m​∣∣​31​=1+2m2−m​​ Case I31​=1+2m2−m​1+2m2=−3m2m2+2m+m+1=02m(m+1)+1(m+1)=0(m+1)(2m+1)=0⇒m=−1 or m=−21​​ If m=–1, then the slopes of the lines are –1 and –2. If m=−21​, then the slopes of the lines are −21​ and −1. Case II​31​=1+2m2m​2m2+1=3m2m2−3m+1=02m2−2m−m+1=02m(m−1)−1(m−1)=0(2m−1)(m−1)=0⇒m=1 or m=21​​ If m=1, then the slopes of the lines are 1 and 2 .If m=21​, then the slopes of the lines are 21​ and 1 .Hence, the slopes of the lines are –1 and –2, or −21​ and –1, or 1 and 2 , or 21​ and 1 .