# How do you write the equation in point slope form given (0,9) and (2,0)?

May 23, 2018

$y = - \frac{9}{2} x + 9$

#### Explanation:

the slope is given by $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ and this is $m = - \frac{9}{2}$
for the equation $y = - \frac{9}{2} x + n$ we get $n$: as $9$

May 23, 2018

$y = - \frac{9}{2} \left(x - 2\right)$

#### Explanation:

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

•color(white)(x)y-y_1=m(x-x_1)

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(0,9)" and } \left({x}_{2} , {y}_{2}\right) = \left(2 , 0\right)$

$m = \frac{0 - 9}{2 - 0} = \frac{- 9}{2} = - \frac{9}{2}$

$\text{using "m=-9/2" and } \left({x}_{1} , {y}_{1}\right) = \left(2 , 0\right)$

$y - 0 = - \frac{9}{2} \left(x - 2\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

$\text{or } y = - \frac{9}{2} \left(x - 2\right)$