Question

Use the graphical method to find the value of \[k\], if \[\left( k,-3 \right)\] lies on straight line
\[2x+3y=1\]
(a) 8
(b) 5
(c) 3
(d) 9

Answer 1

Hint: We solve this problem by creating a table of co – ordinates of points which satisfy the given equation. We take the values of \['y'\] from ‘-4’ to ‘4’ and find the corresponding values of \['x'\] to get the co – ordinates of points as \[\left( x,y \right)\] then we check the value of \['x'\] for which \[y=-3\] because we are given that the co – ordinates of point as \[\left( k,-3 \right)\]

Complete step-by-step answer:
We are given that the equation of line as
\[\begin{align}
  & \Rightarrow 2x+3y=1 \\
 & \Rightarrow x=\dfrac{1-3y}{2} \\
\end{align}\]
Let us take the values of \['y'\] ranging from ‘-4’ to ‘4’ and find the corresponding values of \['x'\]
Let us create a table of these values as follows

\[y\]	4	3	2	1	0	-1	-2	-3	-4
\[x=\dfrac{1-3y}{2}\]	\[\dfrac{-11}{2}\]	-4	\[\dfrac{-5}{2}\]	-1	\[\dfrac{1}{2}\]	2	\[\dfrac{7}{2}\]	5	\[\dfrac{13}{2}\]

Now, by drawing the graph based on above co – ordinates we get

We are given that the co – ordinates of points as \[\left( k,-3 \right)\] which lies on the given straight line
This co – ordinates of point suggests that, at \[x=k\] we have \[y=-3\]
Here, from the table we can see that, at \[x=5\] we have \[y=-3\] or vice versa.
So, by comparing the above two equations we can say that
\[\Rightarrow k=5\]
Therefore the value of \['k'\] is 5

So, the correct answer is “Option (b)”.

Note: This problem can be solved in another way.
We are given that \[\left( k,-3 \right)\] lies on straight line \[2x+3y=1\]
So, by substituting the point in the equation of line we get
\[\begin{align}
  & \Rightarrow 2\left( k \right)+3\left( -3 \right)=1 \\
 & \Rightarrow 2k=1+9 \\
 & \Rightarrow k=5 \\
\end{align}\]
Therefore the value of \['k'\] is 5
So, option (b) is the correct answer.

The above mentioned solution is also correct but it is not the correct solution for the given question because we are told to use graphical methods.
Then we need to find the co – ordinates of points of straight line at random values of either \['x'\] or
\['y'\] to compare the co – ordinated with given point \[\left( k,-3 \right)\] to find the value of \['k'\].