Question

How do you write $y = \dfrac{1}{2}x - 3$ in standard form?

Answer 1

Hint: Here we need to write the given equation in the standard form. We know that the given equation represents the linear equation. So we will use the standard equation of the linear equation here. Then we will perform certain mathematical operations like multiplication and subtraction to simplify the equation and to convert it into the standard form of the linear equation.

Complete step by step solution:
Here we need to write the given equation in the standard form and the given equation is $y = \dfrac{1}{2}x - 3$.
We know that the standard form of the linear equation is given by
$Ax + By = C$
Where, $A$, $B$ and $C$ are integers and $A$ is the non-negative number and also $A$, $B$ and $C$ have no common factors other than 1.
We have to convert the equation $y = \dfrac{1}{2}x - 3$ in the standard form.
So we will first multiply 2 on both sides of the given linear equation.
 $ \Rightarrow 2 \times y = 2 \times \left( {\dfrac{1}{2}x - 3} \right)$
On multiplying the terms, we get
$ \Rightarrow 2 \times y = 2 \times \dfrac{1}{2}x - 2 \times 3 \\
   \Rightarrow 2y = x - 6 \\ $
Now, we will subtract the term $2y$ from both sides.
$ \Rightarrow 2y - 2y = x - 6 - 2y$
On further simplification, we get
$ \Rightarrow 0 = x - 6 - 2y$
We can also write it as
$ \Rightarrow x - 6 - 2y = 0$
Now, we will add 6 to both sides.
$ \Rightarrow x - 6 - 2y + 6 = 0 + 6$
On further simplification, we get

$ \Rightarrow x - 2y = 6$

Hence, this is the standard form of the given linear equation.

Note:
Here, a linear equation is defined as the equation which has the maximum order of 1. The given linear equation has two variables which are also known as the linear equation in two variables and the linear equation also represents the equation of the straight line. If there is only one variable in the equation with the highest degree of 1, then it is termed as a linear equation in one variable. If the highest degree of the equation is 2 then it is called a quadratic equation. Similarly, if the highest degree of the equation is 3 then it is called a cubic equation.