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

Jun 19, 2017

$y + 2 = - 4 \left(x - 0\right)$

#### Explanation:

Begin with finding the slope by using the slope formula: $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

If we let $\left(\textcolor{red}{0} , \textcolor{b l u e}{- 2}\right) \to \left(\textcolor{red}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ and $\left(\textcolor{red}{- 1} , \textcolor{b l u e}{2}\right) \to \left(\textcolor{red}{{x}_{2}} , \textcolor{b l u e}{{y}_{2}}\right)$ then,

$m = \frac{\textcolor{b l u e}{2 - \left(- 2\right)}}{\textcolor{red}{- 1 - 0}} = \frac{4}{-} 1 = - 4$

Using the slope and any of the two points above, we can determine the slope of the line in point-slope form by using this formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$. I will use the point $\left(0 , - 2\right)$

If we let $m = - 4$ and $\left(\textcolor{red}{0} , \textcolor{b l u e}{- 2}\right) \to \left(\textcolor{red}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ then:

$y - \textcolor{b l u e}{\left(- 2\right)} = - 4 \left(x - \textcolor{red}{0}\right)$

$y + 2 = - 4 \left(x - 0\right)$