Question

Draw the graph of following linear equation in two variables:
\[x+y=4\]

Answer 1

Hint: We solve this problem by creating the table of co – ordinates of points that satisfy the given equation. We take the values of \['x'\] from ‘-3’ to ‘3’ and find the corresponding values of \['y'\] to get the co – ordinates of points as \[\left( x,y \right)\] then we consider certain scale of graph and draw the graph using the points.

Complete step-by-step answer:
We are given that the equation of line as
\[\begin{align}
  & \Rightarrow x+y=4 \\
 & \Rightarrow y=4-x \\
\end{align}\]
Let us take the range of \['x'\] from ‘-3’ to ‘3’ and find the corresponding values of \['y'\]
So, for x = -3, we can find y as y = 4 - (-3) = 4 + 3 = 7. Similarly, we will find all other values.
Let us create a table of these values as follows

\[x\]	-3	-2	-1	0	1	2	3
\[y\]	7	6	5	4	3	2	1
\[\left( x,y \right)\]	\[\left( 3,7 \right)\]	\[\left( -2,6 \right)\]	\[\left( -1,5 \right)\]	\[\left( 0,4 \right)\]	\[\left( 1,3 \right)\]	\[\left( 2,2 \right)\]	\[\left( 3,1 \right)\]

Now, let us assume the scale of graph as
On X – axis \[1cm=1unit\]
On Y – axis \[1cm=1unit\]
By using the above scale and co – ordinates of points let us draw the graph then we get

Therefore the graph of the given equation \[x+y=4\] has been completed.

Note: We can draw the graph using some short cut without finding all the co – ordinates.
We find the intercepts that is x – intercept and y – intercept to draw the graph easily.
The x – intercept is calculated by taking \[y=0\]
We are given that the equation of line as
\[\Rightarrow x+y=4\]

By substituting \[y=0\] in given equation we get the x – intercept as
\[\begin{align}
  & \Rightarrow x+0=4 \\
 & \Rightarrow x=4 \\
\end{align}\]
Similarly, we can find the y – intercept by taking \[x=0\]
By substituting \[x=0\] in given equation we get the y – intercept as
\[\begin{align}
  & \Rightarrow 0+y=4 \\
 & \Rightarrow y=4 \\
\end{align}\]
By pointing the x – intercept and y – intercept in graph and joining the points we get the graph as

Here, also we get the same graph but some other part of graph. But, both are same.