Show that the lines `4x+y-9=0,x-2y+3=0,5x-y-6=0` make equal intercepts on any line of slope 2.

Explanation

Let the point meet the given lines in A, B and C

Any lines whose slope is `2` is `y = 2x + c.`


Let it meet the given lines in A, B and C respectively.
Solving with given lines, we get

`A((9−c)/6​,(9+2c)/3​),B((3−2c)/3​,(6−c)/3​)and((6+c​)/3,(12+5c)/3​) `

Clearly A is mid - point of BC so that `BA = AC `

Hence the intercept are equal .