# How do you write an equation in point slope and slope intercept form given (2, 7) and (-2, 9)?

Sep 5, 2017

$y - 7 = - \frac{1}{2} \left(x - 2\right) \text{ and } y = - \frac{1}{2} x + 8$

#### Explanation:

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

•color(white)(x)y-y_1=m(x-x_1)

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

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

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

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

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

$\text{let "(x_1,y_1)=(2,7)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 , 9\right)$

$\Rightarrow m = \frac{9 - 7}{- 2 - 2} = \frac{2}{- 4} = - \frac{1}{2}$

$\text{to obtain the point-slope equation}$

$\text{with "m=-1/2" and } \left({x}_{1} , {y}_{1}\right) = \left(2 , 7\right)$

$y - 7 = - \frac{1}{2} \left(x - 2\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

$\text{rearranging into slope-intercept form}$

$y - 7 = - \frac{1}{2} x + 1$

$\Rightarrow y = - \frac{1}{2} x + 8 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$