Question

How do you write $-3x+y=6$ in standard form?

Answer 1

In this problem we have given the equation of the line and they have asked to write it in the standard form. We have the standard form of the equation of line is $ax+by+c=0$. So, we will rearrange the terms in the given equation. First, we will multiply the given equation with a negative sign on both sides of the equation to get a positive coefficient for variable $x$. Now we will simplify the equation and shift the constant from left side to right side by changing its sign. Then we will get the equation in standard form.

Complete step by step answer:
Given equation, $-3x+y=6$.
Multiplying negative sign with the on both sides of the above equation, then we will get
$\Rightarrow -\left( -3x+y \right)=-6$
We know that when we multiply a negative sign with a negative sign, we will get a positive sign. As well as when we multiply a negative sign with a positive sign then we will get a negative sign. Now the above equation is modified as
$\Rightarrow 3x-y=-6$
Now shifting the constant in the above equation from right side to left side, then we will get
$\Rightarrow 3x-y+6=0$

Hence the standard form of the given equation is $3x-y+6=0$.

Note: We can also write the standard form of the equation by shifting the terms $-3x$, $y$ in left side to right side, then we will get
$\begin{aligned} & \Rightarrow -3x+y=6 \\\ & \Rightarrow 0=3x-y+6 \\\ & \therefore 3x-y+6=0 \\\ \end{aligned}$
From both the methods we got the same result.