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How do you write linear equations in standard form?

Last updated date: 13th Jun 2024
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Hint: As we write the linear equation it is written in more than one form. The most common form is the slope intercept form, but point slope form and standard form also have advantages. In case of any example we determine which form we have to use that is from its unknown value.

Complete step by step solution:
We have,
The standard form of a linear equation,
Whereas, $A,B$ and $C$ are the integers, and also $A$ is non-negative and $A,B,$and $C$ have not any common factor other than $1.$
The most common form is slope intercept form.
The slope of an equation is standard form is:
On other side,
The $y$ intercept of an equation is the standard form is:

Additional Information:
The other way to write slope intercept form is the standard form of equation and the standard form of equation is written as $Ax+By=C.$ As you can also change the slope intercept form is in the standard form. For better understanding we take the example as, $y=\dfrac{-3}{2x}+3$ Now isolate the $y$-intercept and add $\dfrac{3}{2x}$, Now isolate the get, $\dfrac{3}{2x+y}=3$. As we have standard form fraction part does not consider their So, we have to solve it, The equation we get $2\left( \dfrac{3}{2x+y} \right)=3\left( 2 \right)$
$3x+2y=6.$ Then the given equation is considered in a standard form equation.

Note: The standard form of a linear equation is are as follows: $Ax+By=C$ There are some restriction which you need to remember that is $A$ and $B$ cannot be zero and $A$ and $B$ both are integers and $A$ is positive number. In the standard form no fraction nor decimal accepts in the equation. For example we take $\dfrac{1}{3}x+\dfrac{1}{4}y=4$ we can say that the equation is not in the standard form and another example as $4x+3y=8$ then the given equation is in the standard form.