Question

How do you write $\left( y-2 \right)=-\dfrac{1}{2}\left( x-4 \right)$ in standard form.

Answer 1

Hint: We will use the concept of line equation to solve the above question. We know that standard form of linear equation is given as $ax+by=c$, so we will simplify and arrange terms of given equation $\left( y-2 \right)=-\dfrac{1}{2}\left( x-4 \right)$ to write it in standard form. We will first take $-\dfrac{1}{2}$ inside the bracket and multiply it with each term and then we will take ‘x’ term from RHS to LHS towards and take all constant terms to RHS.

Complete step by step answer:
We will use the concept of line equation to solve the above question. We know that the general equation of the line is given as $ax+by=c$, and it is also the standard form of the line equation.
We know from the question that the equation of line is $\left( y-2 \right)=-\dfrac{1}{2}\left( x-4 \right)$, and we have written it in standard form.
So, we will first take $-\dfrac{1}{2}$ inside the bracket and multiply it with each term, then we will get:
$\Rightarrow \left( y-2 \right)=-\dfrac{1}{2}x+2$
Now, we will take x term on the RHS to the LHS and constant term from RHS to LHS.
$\Rightarrow y+\dfrac{1}{2}x=2+2$
$\Rightarrow y+\dfrac{1}{2}x=4$
Now, we will multiply with 2 on both sides of the equation.
$\Rightarrow 2\left( y+\dfrac{1}{2}x \right)=2\times 4$
Now, we will take 2 inside the whole equation, then we will get:
$\Rightarrow 2y+2\times \dfrac{1}{2}x=2\times 4$
$\Rightarrow 2y+x=8$
Hence, 2y + x = 8 is our required standard form of $\left( y-2 \right)=-\dfrac{1}{2}\left( x-4 \right)$.
This is our required solution.

Note:
Students are required to note that when we have a fractional term in line equation then we try to convert it into integral form first and then we will write the standard terms of it by doing simplification.