# How do you write the equation in point slope form given (8,7), (-2,-4)?

Jun 30, 2016

$y + 4 = \frac{11}{10} \left(x + 2\right) .$ [pt.(-2,-4) used]

$y - 7 = \frac{11}{10} \left(x - 8\right) .$ [using pt.(8,7)

#### Explanation:

Let the given pts. be $A \left(8 , 7\right) , B \left(- 2 , - 4\right) .$

Then, by defn., slope of line $A B$ is, by defn., $\frac{{y}_{B} - {y}_{A}}{{x}_{B} - {x}_{A}} = \frac{- 4 - 7}{- 2 - 8} = - \frac{11}{-} 10 = \frac{11}{10.}$

Pt. $B \left(- 2 , - 4\right)$ ies on Line $A B$

Hence, eqn. of line $A B ,$ in slope-pt. form, using pt.$B \left(- 2 , - 4\right) ,$ is :

$y - \left(- 4\right) = \frac{11}{10} \left(x - \left(- 2\right)\right) ,$ i.e., $y + 4 = \frac{11}{10} \left(x + 2\right) .$

One can choose pt.$A \left(8 , 7\right)$ to get the eqn. $y - 7 = \frac{11}{10} \left(x - 8\right) .$