The lines $k_{1}, k_{2}$ and $k_{3}$ represent three different equations as shown in the graph below

Question

The lines $k_{1}, k_{2}$ and $k_{3}$ represent three different equations as shown in the graph below. The solution of the equations represented by the lines $k_{1}$ and $k_{3}$ is $x=3$ and $y=0$ while the solution of the equations represented by the lines $k_{2}$ and $k_{3}$ is $x=4$ and $y=1$.\ Which of these is the equation of the line $k_{3}$ ?\

Professor PC Thomas Classes · Answer

(a) :\ \ ∵ Line $k_{3}$ : $p x+q y=1$ passes through points $(3,0)$ and $(4,1)$\ ∴ We have,\ $3 p=1 \Rightarrow p=\frac{1}{3}$\ and $\frac{1}{3} 	imes 4+q 	imes 1=1 \Rightarrow q=\frac{-1}{3}$ \  ∴ k$_3$ : px + qy =1 $\implies$ x- y  = 3...(1)