Question

How do you write $y = 7x$ in standard form?

Answer 1

This problem deals with solving or actually rewriting the given linear equation which is linear in terms of the variables $x$ and $y$, into a standard form of linear equation. Generally the standard form of a linear equation in two variables is expressed by the equation which is $ax + by + c = 0$, where $a \ne 0$ and $b \ne 0$.

Complete step-by-step solution:
The standard form of the linear equation is given by $ax + by + c = 0$.
The given equation is a linear equation with the variables $x$ and $y$.
The equation which is given to us is $y = 7x$.
Now consider the given equation which is $y = 7x$, as shown below:
$\Rightarrow y = 7x$
Now transfer the term $y$ to the right hand side of the above equation, as shown below:
$\Rightarrow 7x - y = 0$
Now comparing the above equation with the standard form of the linear equation which is $ax + by + c = 0$.
On comparison the given linear equation $7x - y = 0$ with the standard form of the linear equation $ax + by + c = 0$, the coefficients of the given linear equation are given by:
$\Rightarrow a = 7$, $b = - 1$ and $c = 0$
Hence expressing the standard form of equation of the given equation $y = 7x$ is equal to $7x - y = 0$.
The standard form of the equation $y = 7x$ is $7x - y = 0$.

Note: Please note that the above problem is solved by rewriting the given linear equation in two variables into the standard form of linear equation in two variables. This can be done by transferring all the non-zero terms to one side of the equation, and by dividing the equation with the coefficient of $x$ term, in order to make the coefficient of the $x$ term equal to 1.