Question

How do you write the equation \[y=2x-5\] in standard form?

Answer 1

Hint: We know that the standard form of an equation is different for different types of equations. For a quadratic equation \[a{{x}^{2}}+bx=-c\], the standard form of this quadratic equation is \[a{{x}^{2}}+bx+c=0\]. For a linear equation like \[by=ax+c\], the standard form is \[ax-by=-c\]. And for an equation of the form \[y=ax(x-b)+c\], standard form is \[y=a{{x}^{2}}-abx+c\].

Complete step by step answer:
According to the given question, we have to find the standard form of the given equation \[y=2x-5\]. The given equation is same as that of the equation \[by=ax+c\]
Whose standard form is the sum of \[x\] and \[-y\]equal to \[-c\] which is \[ax-by=-c\].
Now let us simplify the given equation to get the standard form.
Given, \[y=2x-5\].
Now we subtract \[y\] from both sides of the equation. then we get
\[\Rightarrow y-y=2x-y-5\]
Now, by subtracting \[y\] from \[y\] we get \[0\]. Then the equation will be
\[\Rightarrow 0=2x-y-5\]
Now we add 5 on both sides of the equation and rearrange the terms in the equation. Then we get
\[\begin{align}
  & \Rightarrow 0+5=2x-y-5+5 \\
 & \Rightarrow 5=2x-y+0 \\
 & \Rightarrow 2x-y=5 \\
\end{align}\]
 On comparing the above equation with \[ax-by=-c\] we get \[a=2\], \[b=1\] and\[c=-5\].
Therefore, the standard form of the equation \[y=2x-5\] is \[2x-y=5\].

Note:
In order to solve such types of questions, one must be aware of the standard form of different equations. We can solve the above equation easily by shifting \[2x\] to the left-hand side of the equation and rearranging the terms gives the standard form of the given equation. While solving such types of problems, general error occurs in the calculation part like changing the sign of variable while shifting.