Question

The path of a train A is given by the equation 3x + 4y − 12 = 0 and the path of another train
B is given by the equation 6x + 8y − 48 = 0. Represent this situation graphically.

Answer 1

We have 

        3x + 4y - 12 = 0 

 ⇒    3x = 12  - 4y 

 ⇒     ${\displaystyle 3x =\frac{12-4y}{3}}$

Putting  y  = 0  We get ${\displaystyle x\frac{12-4\times 0}{3}=4}$

Putting  y = 3 , we get  ${\displaystyle x =\frac{12-4\times 0}{3}=0}$ 

Thus, we have the following table for the points on the line  3x + 4y - 12 =  0 

x	4	0
y	0	3

We have 

 6x + 8y - 48 = 0 

6x + 8y = 48 

6x = 48 - 8y 

${\displaystyle x=48-\frac{8y}{6}}$

Putting  y = 6 , we get  ${\displaystyle x=\frac{48-8\times 6}{6}=0}$

 Putting y = 4 we get ${\displaystyle x=\frac{48-8\times 3}{6}=4}$

Thus, we have the following table for the points on the line 6x + 8y - 48 = 0

x	0	4
y	6	3