Question

How do you graph the equation by plotting points \[2x - 2y = 6\]?

Answer 1

Hint: The given equation is a linear equation and so obtain at least two points that satisfy the given linear equation and plot those points on the rectangular Cartesian coordinate system and draw a line that passes through them.

Complete step by step solution:
Write the given linear equation.
\[2x - 2y = 6\] …… (1)

Isolate one of the variables and express it in terms of the other variable.

Here, we isolate the variable \[x\] in terms of the variable \[y\]as follows:

Add \[2y\] to both sides of the linear equation (1) as shown below.
\[ \Rightarrow 2x - 2y + 2y = 6 + 2y\]
\[ \Rightarrow 2x = 6 + 2y\]

Now, divide the above obtained equation by \[2\] and simplify as shown below.
\[ \Rightarrow \dfrac{{2x}}{2} = \dfrac{{6 + 2y}}{2}\]
\[ \Rightarrow x = \dfrac{6}{2} + \dfrac{{2y}}{2}\]
\[ \Rightarrow x = 3 + y\]

Therefore, we can write the equation (1) as \[x = 3 + y\].

Now, obtain at least two points by substituting two appropriate values of variable \[y\] and obtain the corresponding values of \[x\] as shown below.

Substitute \[y\] as \[0\] in the transformed equation \[x = 3 + y\] and obtain the value of \[x\],
\[\begin{array}{c}x = 3 + \left( 0 \right)\\ = 3\end{array}\]

Similarly, substitute \[y\] as \[2\] in the transformed equation \[x = 3 + y\] and obtain the value of \[x\],
\[\begin{array}{c}x = 3 + \left( 2 \right)\\= 5\end{array}\]

So, the two points to sketch the graph of a given linear equation are \[\left( {3,0} \right)\] and \[\left( {5,3} \right)\] in the form \[\left( {x,y} \right)\].

Therefore, sketch the graph of given linear equation \[2x - 2y = 6\] by locating two points \[\left( {3,0} \right)\] and \[\left( {5,3} \right)\] in the Cartesian plane and draw a line that passes through these two points as shown in the below figure.

So, this is the right way to plot a graph of a given linear equation by plotting points on a Cartesian plane.

Note: Linear equations in two variables have infinite solutions or say points that can satisfy the equation so you can find any two of them to plot a graph or line of that linear equation.