# How do you write the equation in point slope form given (0,-2) with slope = -3/7?

May 27, 2016

$y + 2 = m \left(x - 0\right) \text{ } \leftarrow$ In full form

$y + 2 = m x \text{ } \leftarrow$ In simplified form

#### Explanation:

For any given point ${P}_{i} \to \left({x}_{i} , {y}_{i}\right) \text{ and gradient } m$

We have $y - {y}_{i} = m \left(x - {x}_{i}\right)$

In other words you are looking just at the gradiant.

There is no need to worry about the $c$ in $y = m x + c$ as it is implied and locked into the condition $y - {y}_{i} = m \left(x - {x}_{i}\right)$. You can only have one value for $c$ to make $\left({x}_{i} , {y}_{i}\right)$ work.

So for your question we have:

Given that ${P}_{i} \to \left({x}_{i} , {y}_{i}\right) \to \left(0 , - 2\right)$

$\textcolor{b r o w n}{y - {y}_{i} = m \left(x - {x}_{i}\right)} \textcolor{b l u e}{\text{ "->" } y - {\left(- 2\right)}_{i} = m \left(x - 0\right)}$

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