Question

How do you create a table using the equation $2x-6y=12$ ?

Answer 1

Hint: To create a table, we need two variables in an equation. In the given equation $2x-6y=12$ , there are two variables that are $x$ and $y$ . So, we can create the value of one variable by putting the value of another variable that shows the relation between these two variables and that also shows the points from which the line goes on.

Complete step by step answer:
Since, we have the given equation $2x-6y=12$ in the form of a linear equation that describes the relationship between the variables $x$ and $y$ .
So, we can create a table that has the values of the variables $x$ and $y$respectively by putting the value in any one of the variables may be $x$ or $y$ and we will find other values by calculating the linear equation.
Since, we have the linear equation as:
$\Rightarrow 2x-6y=12$
Now, we will change it as:
$\Rightarrow 2x=12+6y$
Since, $2$ is the common factor in the above equation. So after dividing by $2$ in the above equation we have as:
$\Rightarrow \dfrac{2x}{2}=\dfrac{12+6y}{2}$
Now, we will simplify the above equation as:
$\Rightarrow \dfrac{2x}{2}=\dfrac{12}{2}+\dfrac{6y}{2}$
$\Rightarrow x=6+3y$
Now, we can create the table using the equation $x=6+3y$ as:

Value of $y$	Putting the value of $y$ in the equation $x=6+3y$ to get the value of $x$	Value of $x$
1	$x=6+3\times \left( 1 \right)$	9
2	$x=6+3\times \left( 2 \right)$	12
3	$x=6+3\times \left( 3 \right)$	15
4	$x=6+3\times \left( 4 \right)$	18
5	$x=6+3\times \left( 5 \right)$	21
6	$x=6+3\times \left( 6 \right)$	24
7	$x=6+3\times \left( 7 \right)$	27
8	$x=6+3\times \left( 8 \right)$	30
9	$x=6+3\times \left( 9 \right)$	33
10	$x=6+3\times \left( 10 \right)$	36

Since, this is a table of values up to 10 but it will be continued.
Hence, the given equation defines the relation between $x$ and $y$ by creating the table of the values that are true for the given equation.

Note:
 Since we created the table of the linear equation $2x-6y=12$ by putting the value for $y$, we will verify the values by inverse method. Here we will put the values for $x$ and will get a value of $y$ .
We have the equation as: $2x-6y=12$
We will change it as:
$\Rightarrow 2x-12=6y$
\[\Rightarrow y=\dfrac{x}{3}-2\]
Now, we can verify by creating this table:

Value of $x$	Putting the value of $y$ in the equation \[y=\dfrac{x}{3}-2\] to get the value of $x$	Value of $y$
9	\[y=\dfrac{9}{3}-2\]	1
12	\[y=\dfrac{12}{3}-2\]	2
15	\[y=\dfrac{15}{3}-2\]	3
18	\[y=\dfrac{18}{3}-2\]	4
21	\[y=\dfrac{21}{3}-2\]	5
24	\[y=\dfrac{24}{3}-2\]	6
27	\[y=\dfrac{27}{3}-2\]	7
30	\[y=\dfrac{30}{3}-2\]	8
33	\[y=\dfrac{33}{3}-2\]	9
36	\[y=\dfrac{36}{3}-2\]	10

Hence, the solution is verified.