Question

How do you write the equation $y+3=3\left( x+5 \right)$ in standard form?

Answer 1

Hint: For answering this question we need to write the given straight line equation $y+3=3\left( x+5 \right)$ in the standard form which is generally given as $ax+by=c$ where $\dfrac{-a}{b}$ is the slope of the corresponding straight line.

Complete step by step answer:
Now considering from the question we have been asked to write the given straight line equation $y+3=3\left( x+5 \right)$ in the standard form which is generally given as $ax+by=c$ where $\dfrac{-a}{b}$ is the slope of the corresponding straight line.
Now for doing this we will perform some simple arithmetic operations. Firstly we will multiply $3$ with $\left( x+5 \right)$ , after doing that we will have $\Rightarrow y+3=3x+15$
Now by further simplifying this expression we will have $\Rightarrow 3x-y-3+15=0$ .
Now we will shift $-3+15$ from the left hand side to the right hand side of the given expression. After doing that we will have $\Rightarrow 3x-y=3-15$ .
Now we will add the terms on the right hand side of this equation to simplify it further. After doing that we will have $\Rightarrow 3x-y=-12$ .

Therefore we can conclude that the standard form of the given straight line equation $y+3=3\left( x+5 \right)$ will be given as $3x-y=-12$.

Note: In the process of answering questions of this type we should be careful with the calculations we perform during the process. Someone can make a mistake during solving this question and consider it as
$\begin{align}
  & y+3=3\left( x+5 \right) \\
 & \Rightarrow y+3=3x+15 \\
 & \Rightarrow y-3x=12 \\
\end{align}$
which will lead us to end up having a wrong conclusion.