
Can an equation in standard form have fractions ?
Answer
411.6k+ views
Hint: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 where , and are integers and also 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
The standard form of the equation
On subtracting on both sides,
We get ,
On simplifying,
We get,
On dividing both sides by ,
We get,
Thus , the standard form of the equation will be
The slope of the standard form of the equation is
On the other side the y intercept of the standard form of the equation is
For example let us consider an equation
Now on multiplying both sides by ,
We get,
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 . There are some restrictions for the standard form of the equation which we have to remember that and cannot be zero and and both are integers and 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.
Complete step by step solution:
The standard form of the equation is
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
The standard form of the equation
On subtracting
We get ,
On simplifying,
We get,
On dividing both sides by
We get,
Thus , the standard form of the equation will be
The slope of the standard form of the equation is
On the other side the y intercept of the standard form of the equation is
For example let us consider an equation
Now on multiplying both sides by
We get,
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
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