Question

How do you write $y = \dfrac{5}{6}x + \dfrac{5}{{12}}$ in standard form ?

Answer 1

In this question, we need to write the given expression in the standard form. If we carefully observe the given equation, it is in the form of $y = mx + c$. We try to write it in a standard form of a linear equation which is given by, $Ax + By + C = 0$. Hence, we make rearrangement in the given equation and try to convert it in the general form. After that, we will get the solution in the standard form which is the required answer.

Complete step by step solution:
Let us solve the question.
Given an equation of the form $y = \dfrac{5}{6}x + \dfrac{5}{{12}}$ …… (1)
We are asked to find the standard form of the above expression given in the equation (1).
Observe the given equation carefully.
Note that it is in the form of $y = mx + c$, which is the slope intercept form of a straight line.
where m is the slope and c is the y-intercept of the line.
We know that the standard form of a linear equation is given by,
$Ax + By + C = 0$ …… (2)
Where, if at all possible A, B and C are integers and A is non negative.
Also A, B and C have no common factor other than 1.
Now we will convert the given equation into standard form.
From equation (1), we have,
$y = \dfrac{5}{6}x + \dfrac{5}{{12}}$
Now take the LCM on the R.H.S. we get,
$\Rightarrow y = \dfrac{{10x + 5}}{{12}}$
Multiply by 12 on both the sides we get,
$\Rightarrow 12 \times y = 12 \times \dfrac{{10x + 5}}{{12}}$
Simplifying we get,
$\Rightarrow 12y = 10x + 5$
Subtract $12y$ on both sides we get,
$\Rightarrow 12y - 12y = 10x + 5 - 12y$
Combining like terms $12y - 12y = 0$
$\Rightarrow 0 = 10x + 5 - 12y$
After rearrangement we get the equation of the form,
$\Rightarrow 10x - 12y + 5 = 0$
Which is in the standard form of a linear equation.

Hence, the standard form of an equation $y = \dfrac{5}{6}x + \dfrac{5}{{12}}$ is given by $10x - 12y + 5 = 0$.

Note :
Student must remember the standard form of a linear equation which is given as,
$Ax + By + C = 0$
Where, if at all possible A, B and C are integers and A is non negative.
Also A, B and C have no common factor other than 1.
To get an equation into standard form, follow the steps given below.
(1) Isolate the constant term i.e. the term with no variable on the right hand side of the equation by just adding and subtracting terms from both sides.
(2) If there are any fractions involved, multiply the whole equation by the lowest common denominator.
(3) If the coefficient of A is negative, then multiply the whole equation by -1.