Question

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

Answer 1

Find standard equation:

Standard form of a linear equation is defined by $ax+by+c=0$, where $a$, $b$ and $c$ are constants to be determined.

Given equation is $y-2=-\frac{1}{2}\left(x-4\right)$.

Cross multiplying both sides of the equation, we get

$$\begin{gathered} \Rightarrow y-2=-\frac{1}{2}\left(x-4\right) \\ \Rightarrow 2\left(y-2\right)=-1\left(x-4\right)\left[\mathrm{On}\mathrm{cross}\mathrm{multiplication}\right] \\ \Rightarrow 2y-4=-x+4\left[\mathrm{Remove}\mathrm{brackets}\right] \\ \Rightarrow x+2y=4+4\left[\mathrm{Arranging}\mathrm{variables}\mathrm{on}\mathrm{left}\mathrm{side}\mathrm{and}\mathrm{constant}\mathrm{on}\mathrm{right}\mathrm{side}\right] \\ \therefore x+2y-8=0 \end{gathered}$$

Obtained equation is of the form $ax+by-c=0$.

Hence, the standard equation is $x+2y-8=0$.