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

$\text{Path of the train}A\to 3x+4y-12=0\text{Path of the train}B\to 6x+8y-48=0Now,3x+4y-12=0\Rightarrow 3x=12-4y\Rightarrow x=\frac{12-4y}{3}Ify=0,thenx=\frac{12-4\times 0}{3}=\frac{12-0}{3}=\frac{12}{3}=4Ify=3,thenx=\frac{12-4\times 3}{3}=\frac{12-12}{3}=\frac{0}{3}=0\begin{array}{ccc}x& 4& 0\\ y& 0& 3\end{array}$

Now plot the points (4, 0) and (0, 3) on the graph and join them to get a line.

Now, $6x+8y-48=0\Rightarrow 6x=48-8y$

$\Rightarrow x=\frac{48-8y}{6}Ify=6,thenx=\frac{48-8\times 6}{6}=\frac{48-48}{6}=\frac{0}{6}=0Ify=3,thenx=\frac{48-8\times 3}{6}=\frac{48-24}{6}=\frac{24}{6}=4\begin{array}{ccc}x& 0& 4\\ y& 6& 3\end{array}$

Now plot the points (0, 6) and (4, 3) on the graph and join them to get another linc.