Question

How do you write $y = 3x + 1$ in a standard form?

Answer 1

Hint: To solve this, we need to find what kind of equation and then we can discuss the standard
form of the equation. So the given equation here is linear equation of for $Ax + By = C$ so we are going
to change the given equation to this form by subtracting and multiplying with $ - 3x$ and $ - 1$ respectively.
Then after reducing the equation we will get the standard form of the given equation.

Complete step-by-step solution:
The given equation is a linear equation of form $Ax + By = C$
Where $A$ ,$B$ and $C$ are constants with $A$ and $B$ which is not equal to zero.
Let us now rearrange the given equation in $Ax + By = C$ form
$ \Rightarrow y = 3x + 1$
From the given above equation, we are going to Subtract both sides by $3x$
$\therefore - 3x + y = - 3x + 3x + 1$
Then, We will get
$ \Rightarrow - 3x + y = 1$
Now, multiplying both the sides by $ - 1$ to make the x coefficient positive
$ \Rightarrow - 1( - 3x + y) = - 1 \times 1$
Then multiplying $ - 1$ inside the brackets, we will get
$ \Rightarrow ( - 1 \times - 3x) + ( - 1 \times y) = - 1$
On reducing this, we will get
$ \Rightarrow 3x - 1y = - 1$

Hence we get the standard form of equation of $y = 3x + 1$ is $3x - 1y = - 1$

Note: If you compare the results to the standard form, you will see that it is the same form in which
$A = 3$ $B = - 1$ and $C = - 1$ .Hope this helps you to understand how to arrange linear equations with
two variables into standard form. And also equations in standard form follow the structure: $Ax + By = C$
$A$ ,$B$ and C are all integers. $'A'$ should always be positive. To get an equation into standard form, just follow these
steps:
Isolate the constant (the term with no variable) on the right side of the equation by just adding and subtracting terms from both sides.
If there are any fractions, multiply the whole equation by the lowest common denominator.
If the constant in the A position is negative, multiply the whole equation by −1.