# How do you write the point slope form of the equation given (0,2) and (2,1)?

Aug 10, 2017

The equation is $y - 2 = - \frac{1}{2} \left(x - 0\right)$

#### Explanation:

Point slope form of equation is $y - {y}_{1} = m \left(x - {x}_{1}\right)$, which represents equation of a line passing through point $\left({x}_{1} , {y}_{1}\right)$ and having a slope $m$.

As slope of line joining $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, slope of line joining $\left(0 , 2\right)$ and $\left(2 , 1\right)$ is $\frac{1 - 2}{2 - 0} = - \frac{1}{2}$.

Hence, slope of desired line is $- \frac{1}{2}$ and as it passed through $\left(0 , 2\right)$, point slope form of its equation is

$y - 2 = - \frac{1}{2} \left(x - 0\right)$

or $2 y - 4 = - x$ or $x + 2 y - 4 = 0$