If the lines y=3 x+1 and 2 y=x+3 are equally inclined to the line y=m x+4 , then the value of ' m ' is equal to

Step-by-step solution

Given Lines are, aligned & y=3 x+1 m₁=3 2 y=x+3 & y= 1 2 x+ 3 2 m₂= 1 2 & y=m x+4 aligned According to the question, | m₁-m 1+m₁ m |= | m₂-m 1+m₂ m | . Angle between lines is . = | m₁-m₂ 1+m₁ m₂ | aligned & | 3-m 1+3 m |= | 1 2 -m 1+ 1 2 m | & | 3-m 1+3 m |= | 1-2 m 2+m | & 3-m 1+3 m = | 1-2 m 2+m | aligned Case (i) aligned 3-m 1+3 m & =- ( 1-2 m 2+m ) (3-m)(2+m) & =(2 m-1)(1+3 m) 6+m-m^2 & =6 m^2-m-1 7 m^2-2 m-7 & =0 m & = 2 (-2)^2-4 7(-7) 2 7 & = 2 4+196 14 = 2 10 2 14 = 1 5 2 7 m & = 1 5 2 7 aligned Hence, optio