How do you write the equation in point slope form given (4,5) and (-3,8)?

Jun 3, 2017

$y - 5 = - \frac{3}{7} \left(x - 4\right)$

Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

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

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

$\text{the points are } \left({x}_{1} , {y}_{1}\right) = \left(4 , 5\right) , \left({x}_{2} , {y}_{2}\right) = \left(- 3 , 8\right)$

$\Rightarrow m = \frac{8 - 5}{- 3 - 4} = \frac{3}{- 7} = - \frac{3}{7}$

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

$\text{using " (x_1,y_1)=(4,5)" and } m = - \frac{3}{7}$

$\Rightarrow y - 5 = - \frac{3}{7} \left(x - 4\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$