Question

Write $y = 2x - 4$ in standard form ?

Answer 1

Hint: Here, in the given question, we are given a linear equation (an equation is said to be a linear equation in two variables if it is written in the form of $Ax + By = C$). In this question we have to write the given equation in the standard form, we know that the standard form of the linear equation is given by $Ax + By = C$ where, if at all possible, $A$, $B$, and $C$ are integers, and $A$ is non-negative term, and $A$, $B$, and $C$ have no common factors other than $1$ and now substituting the values in the form we will get the required answer.

Complete step by step answer:
Given equation, $y = 2x - 4$. Rewrite the given equation by subtracting $2x$ from both the sides of the equation.
$ \Rightarrow y - 2x = 2x - 4 - 2x$
On subtraction of like terms, we get
$ \Rightarrow y - 2x = - 4$
We can also multiply the given equation by $ - 1$.
$ \Rightarrow - 1\left( {y - 2x} \right) = - 1 \times - 4$
On multiplication of terms, we get
$ \Rightarrow - y + 2x = 4$
We can also write it as,
$ \therefore 2x - y = 4$

Therefore, the standard form of the given equation $y = 2x - 4$ will be equal to $ - 2x + y = - 4$ or $2x - y = 4$.

Note: Linear equations represent a straight line. Linear equations in two variables make it easy to explain the geometry of the lines or the graph of two lines or equations, it contains two variables whose values are unknown. The linear equations of two variables can be solved by converting the situation into mathematical statements which tell the relation between the unknown variables and it makes it easier to solve such problems. We should take care of the calculations so as to be sure of our final answer.