given the linear equation 3x+4y-5=0,write another equation in 2 variable such that the geometrical representation of the pair so formed is 1) intersecting lines 2) parallel lines 3) coincident lines

given the linear equation 3x+4y-5=0,write another equation in 2 variable such that the geometrical representation of the pair so formed is 1) intersecting lines 2) parallel lines 3) coincident lines

equation can be find out if we compare the ratios  =  = 

now we have the equation 3x + 4y – 5 = 0

we know if,   , lines are intersecting

so we can get any equation keeping the above equation in mind

 5x + 2y – 8 = 0

Here  , hence 

5x + 2y – 8 = 0 and 3x + 4y – 5 = 0 are intersecting lines

2). Now

We know if  =  , lines are parallel

  So another equation can be

6x + 8y + 2 = 0

Here,  =  

   =  

Hence, 6x + 8y + 2 = 0 and 3x + 4y – 5 = 0  are parallel lines

3). For coincidental lines,

 If  =  = , lines are coincidental

So, another line can be

9x + 12y – 15 = 0

Here ,  =  = 

   =  = 

Hence , 9x + 12y – 15 = 0  and 3x + 4y – 5 = 0   are coincidental lines