Question

Draw the graph of the equation $ y - x = 2 $ .

Answer 1

Hint: To draw a graph of a linear equation. We first assume some value of either of the variables and then using these values on substituting in the given linear equation we calculate the values of other variables and then plotting these points in x-y plane we will have a required graph of the given equation.

Complete step-by-step answer:
To draw a graph of a linear equation. We first assume some value of either of the variables and then using these values on substituting in the given linear equation we calculate the values of other variables.
Then plotting these values of ‘x’ and ‘y’ on the x-y plane.
Joining of these plotted points gives a graph of the given linear equation.
We first let different values of ‘x’. Which are
For $ x = 1 $ , on substituting in $ y - x = 2 $ we have
 $
 y - 1 = 2 \\
 \Rightarrow y = 2 + 1 \\
 \Rightarrow y = 3 \;
  $
Therefore, for $ x = 1 $ we have $ y = 3 $
For, on substituting in $ y - x = 2 $ we have
 $
 y - 2 = 2 \\
 \Rightarrow y = 2 + 2 \\
 \Rightarrow y = 4 \;
  $
Therefore, for $ x = 2 $ we have $ y = 4 $
For, on substituting in $ y - x = 2 $ we have
 $
 y - 3 = 2 \\
 \Rightarrow y = 2 + 3 \\
 \Rightarrow y = 5 \;
  $
Therefore, $ x = 3 $ for we have $ y = 5 $

x	1	2	3
y	3	4	5

Note: Graph of a linear equation is always a straight line. If while calculating points if someone has made a mistake then all the points obtained after calculations will not come on a straight line. So, one should do calculation carefully while doing calculation for points and also while plotting in x-y plane.