# How do you write the point slope form of the equation given (-3,-3) and slope -1/3?

Aug 10, 2016

$y = \frac{- 1}{3} x - 4$

#### Explanation:

There is a very nifty formula for exactly this situation where we are given the slope $\left(m\right)$ and one point $\left({x}_{1} , {y}_{1}\right)$ on a straight line and need to find its equation.

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y \textcolor{red}{- \left(- 3\right)} = \frac{- 1}{3} \left(x \textcolor{red}{- \left(- 3\right)}\right) \text{ simplify}$

$y \textcolor{red}{+ 3} = \frac{- 1}{3} \left(x \textcolor{red}{+ 3}\right)$

$y \textcolor{b l u e}{+ 3} = \frac{- 1}{3} x - 1$

$y = \frac{- 1}{3} x - 1 \textcolor{b l u e}{- 3}$

$y = \frac{- 1}{3} x - 4$

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Note that the formula is based on the formula for slope

$y - {y}_{1} = m \left(x - {x}_{1}\right)$ is derived from $\frac{y - {y}_{1}}{x - {x}_{1}} = m$
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We could also have substituted the given values into $y - m x + c$
to find $c$ and then substituted again for the final answer.

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