The path of a wheel of train A is given by the equation

x+2y−4=0
and the path of a wheel of another train B is given by the equation

2x+4y−12=0
. When we represent this situation geometrically, we infer that these two lines are ____.

Question

The path of a wheel of train A is given by the equation

x+2y−4=0
   and the path of a wheel of another train B is given by the equation

2x+4y−12=0
  . When we represent this situation geometrically, we infer that these two lines are ____.

Accepted Answer

The path of a wheel of train A is given by the equation $x + 2 y − 4 = 0$ and the path of a wheel of another train B is given by the equation $2 x + 4 y − 12 = 0$ . When we represent this situation geometrically, we infer that these two lines are ____.

x+2y−4=0                       ......(1)

⇒2y=4−x

⇒y=
      
       4−x
      2

And the path of a wheel of another train B is given by the equation

2x+4y−12=0                       ......(2)

⇒4y=12−2x

⇒y=
      
       12−2x
      4

From equation 1, we get,

y=
    
     4−x
    2

. Then table for

x + 2y−4=0
   is,So, the points are

0,2
   ,
    
     4,0
   
   and

2,1
   
  .From equation 2, we get

y = 
    
     12−2x
    4

. Then table for

2x + 4y − 12 = 0
   is, So, the points are

0,3
   ,
    
     6,0
   
   and

2,2
   
  . On plotting points

0,2
   ,
    
     4,0
   and
    
     2,1
   
   and

0,3
   ,
    
     6,0
   and
    
     2,2
   
   on the graph paper and joining them by a line, we get the following graph for the above equations.In the graph, we observed that these two lines did not intersect anywhere. Hence, these two lines are parallel.