Question

Can an equation in standard form have fractions ?

Answer 1

In this question, we need to explain if an equation in standard form has fractions . The other method to write the linear equation is the standard form. The most common form is the slope intercept form, but point slope form and standard form also have advantages. We know how to find out the slope when the standard form of the equation is given. Then let us consider an equation with fractions to check if an equation in standard form has fractions or not.

Complete step by step solution:
The standard form of the equation is $Ax + By + C = 0$ where $A$, $B$ and $C$ are integers and also $A$ is a non negative integer.
The most common form of the standard form of equation is the slope intercept form.
Slope-intercept form and the point-slope form of the linear equation both contain the slope of the equation but the standard form does not contain the slope. Since the slope is such an important feature of a line, it is important to know how to find out the slope when the standard form of the equation is given.
The slope intercept form is $y = mx + b$
The standard form of the equation $Ax + By = C$
On subtracting $Ax$ on both sides,
We get ,
$\Rightarrow \ Ax – Ax + By = C – Ax$
On simplifying,
We get,
$\Rightarrow \ By = C – Ax$
On dividing both sides by $B$,
We get,
$\Rightarrow \dfrac{By}{B} = \dfrac{C – Ax}{B}$
Thus , the standard form of the equation will be
$y = - \dfrac{A}{B}x + \dfrac{C}{B}$
The slope of the standard form of the equation is
$\Rightarrow \ m = - \dfrac{A}{B}$
On the other side the y intercept of the standard form of the equation is
$\Rightarrow \dfrac{C}{B}$
For example let us consider an equation $x – 2y + \dfrac{9}{4} = 0$
Now on multiplying both sides by $4$ ,
We get,
$\Rightarrow \ 4x – 8y + 9 = 0$
Thus the equation is in the standard form with no fractions.
Equations written in standard form can never have fractions.

Note:
The standard form of the equation can also be written as $Ax + By = C$. There are some restrictions for the standard form of the equation which we have to remember that $A$ and $B$ cannot be zero and $A$ and $B$ both are integers and $A$ is a positive number. Also , the standard form of the equation never has decimals . According to the definition of standard form, the coefficients of the equation must be integers. So we need to clear the fractions in the equation.