Question

Express the linear equation $3x = y$ in the form of $ax + by + c = 0$ and write values of $a,b$ and $c$ .

Answer 1

Hint: The given equation should be arranged and represented in the form of $ax + by + c = 0$ by shifting the variables and changing the signs, then the resultant new equation is compared with the standard equation for finding the values of $a,b$ and $c$.

Complete step-by-step answer:
According to the question we are given linear equation as $3x = y$ and we have to express it the form of $ax + by + c = 0$
As we can see we have the terms containing $x$ and $y$ in our equation, but we do not have any term without the variable that is the constant term , so we will assume the constant term as $0$.
So, we have the equation as
$3x = y$
Now rearranging and taking the term to left hand side by changing the sign of the term and adding constant term we get the equation as,
$3x - y + 0 = 0\,\,\,\,$
$ \Rightarrow \,\,3x + \left( { - y} \right) + 0 = 0\,\,\,\,\,\,$
$ \Rightarrow \,\,\,3x + \left( { - 1} \right)y + 0 = 0……………......\left( i \right)$
This the new equation
And we are given the standard linear equation as
$ax + by + c = 0$

Comparing equation $\left( i \right)$ with the standard equation we get the values of $a,b$ and $c$ as $a = 3,\,\,b = - 1\,\,$ and $c = 0$.

Note: Any equation of the form $ax + by + c = 0$ where $a,b,c$ are any constant numbers is called the linear equation in two variables provided $a$ and $b$ are non-zero. It is the general equation of the line. Any line plotted on the graph of the linear equation is always a straight line.
The equation could be given to us in any form, with one variable $x$ or with two variables $x$ and $y$, and to represent it in standard form of linear equation, we have to assume the terms as zero, if the equation is without a variable. For example, if the equation given is $3x = 4$ then here the term containing $y$ variable is missing. So, we will assume it as $0y$ and the equation thus becomes $3x + 0y - 4 = 0$.