Question

How do you graph $ x - y = 6 $ ?

Answer 1

Hint: Here in this given equation first we rearrange the equation shift the variable x to the RHS keep y in LHS now give the values to the x like 0, 1, 2, 3, … simultaneously we get the values of y. Now we get the coordinates of the given equation i.e., (x,y) by using the coordinates to construct the graph. We assign the value of x and we determine the value of y and we plot the graph.

Complete step-by-step answer:
Given equation in the form of linear equation in the form of two variables x and y
Consider the equation $ x - y = 6 $
For this equation, we first solve the equation by starting with moving the x in the equation to the other side i.e., RHS or subtracting x on both side, we get
 $ - y = 6 - x $
In the above equation 2 variables x and y are there
By giving the x values 0, 1, 2, 3, … simultaneously we get the values of y
Put x=0
Then $ \Rightarrow \, - y = 6 - 0 $
 $ \therefore \,\,\,y = - 6 $
Therefore, coordinate $ \left( {x,y} \right) = \left( {0, - 6} \right) $
Put x=2
 $ \Rightarrow \, - y = 6 - 2 $
 $ \therefore \,\,\,y = - 4 $
 Therefore, coordinate $ \left( {x,y} \right) = \left( {2, - 4} \right) $
Put x=4
 $ \Rightarrow \, - y = 6 - 4 $
 $ \therefore \,\,\,y = - 2 $
 Therefore, coordinate $ \left( {x,y} \right) = \left( {4, - 2} \right) $
Put x=6
 $ \Rightarrow \, - y = 6 - 6 $
 $ \therefore \,\,\,y = 0 $
 Therefore, coordinate $ \left( {x,y} \right) = \left( {6,0} \right) $
Put x=8
 $ \Rightarrow \, - y = 6 - 8 $
 $ \therefore \,\,\,y = 2 $
 Therefore, coordinate $ \left( {x,y} \right) = \left( {8,2} \right) $
And so on
The coordinates can be written in table as :

$ x $	$ 0 $	$ 2 $	$ 4 $	$ 6 $	$ 8 $
$ y $	$ - 6 $	$ - 4 $	$ - 2 $	$ 0 $	$ 2 $
$ \left( {x,y} \right) $	$ \left( {0, - 6} \right) $	$ \left( {2, - 4} \right) $	$ \left( {4, - 2} \right) $	$ \left( {6,0} \right) $	$ \left( {8,2} \right) $

Now, the graph of the given linear equation $ x - y = 6 $ by using the above table as follows:

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. By the given equation write it for y and consider it as a graph equation. By the equation of a graph, we can plot the graph by assuming the value of x. we can’t assume the value of y. because the value of y depends on the value of x. Hence, we have plotted the graph.