# How do you write the equation in point slope form given (-3,-5) and (3,-15)?

Mar 23, 2018

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

#### 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)

$\text{let "(x_1,y_1)=(-3,-5)" and } \left({x}_{2} , {y}_{2}\right) = \left(3 , - 15\right)$

$\Rightarrow m = \frac{- 15 - \left(- 5\right)}{3 - \left(- 3\right)} = \frac{- 10}{6} = - \frac{5}{3}$

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

$\text{using "m=-5/3" and } \left({x}_{1} , {y}_{1}\right) = \left(- 3 , - 5\right)$

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

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

Mar 23, 2018

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

#### Explanation:

Point slope form is $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
First, find the slope by using $m = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}$
$\frac{- 15 + 5}{3 + 3} = - \frac{10}{6} = - \frac{5}{3} = m$
Then, choose one of the coordinate pairs (let's use $- 3 , - 5$) and plug those in for ${y}_{1}$ and ${x}_{1}$ and also plug in the slope for $m$.
We get: $\left(y + 5\right) = - \frac{5}{3} \left(x + 3\right)$