# How do you write the point slope form of the equation given (0,3) and (-1,-3)?

May 3, 2017

$y + 3 = 6 \left(x + 1\right)$

#### Explanation:

$\text{the equation of a line in "color(blue)"point-slope form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where m represents the slope and " (x_1,y_1)" a point on the line}$

$\text{to calculate the slope use the "color(blue)"gradient formula}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where " (x_1,y_1),(x_2,y_2)" are 2 points on the line}$

$\text{the 2 points here are " (0,3)" and } \left(- 1 , - 3\right)$

$\text{let " (x_1,y_1)=(0,3)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 1 , - 3\right)$

$\Rightarrow m = \frac{- 3 - 3}{- 1 - 0} = \frac{- 6}{- 1} = 6$

$\text{use either of the 2 given points for } \left({x}_{1} , {y}_{1}\right)$

$\text{using " m=6" and } \left({x}_{1} , {y}_{1}\right) = \left(- 1 , - 3\right)$

y-(-3)=6(x-(-1)larr"substitute in equation"

$\Rightarrow y + 3 = 6 \left(x + 1\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$