# How do you write the equation in point slope form given (-2,-8) and slope 5/6?

Mar 24, 2017

$\frac{y + 8}{x + 2} = \frac{5}{6}$

#### Explanation:

Given a point $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$ and a slope of $\textcolor{g r e e n}{m}$
the slope-point form may be written as:
$\textcolor{w h i t e}{\text{XXX}} \frac{y - \textcolor{b l u e}{b}}{x - \textcolor{red}{a}} = \textcolor{g r e e n}{m}$
or (equivalently)
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{b} = \textcolor{g r e e n}{m} \left(x - \textcolor{red}{a}\right)$

Substituting $\left(\textcolor{red}{- 2} , \textcolor{b l u e}{- 8}\right)$ for $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$ and $\textcolor{g r e e n}{\frac{5}{6}}$ for $\textcolor{g r e e n}{m}$
we get
$\textcolor{w h i t e}{\text{XXX}} \frac{y \textcolor{b l u e}{+ 8}}{x \textcolor{red}{+ 2}} = \textcolor{g r e e n}{\frac{5}{6}}$
or
$\textcolor{w h i t e}{\text{XXX}} y \textcolor{b l u e}{+ 8} = \textcolor{g r e e n}{\frac{5}{6}} \left(x \textcolor{red}{+ 2}\right)$

Warning: Check with your instructor; he/she may want the factors left in explicit point form, namely: (y-color(blue)(""(-8))) and (x-color(red)(""(-2)))

Mar 24, 2017

The equation of the line is $y = \frac{5}{6} x - 6 \frac{1}{3}$

#### Explanation:

Let the equation of the line be y=mx+c ; m= 5/6 :. y=5/6x+c.

The point $\left(- 2 , - 8\right)$ will satisfy the equation. $\therefore - 8 = \frac{5}{6} \cdot \left(- 2\right) + c \therefore c = \frac{10}{6} - 8 = - \frac{38}{6} = - \frac{19}{3} = - 6 \frac{1}{3} \therefore y = \frac{5}{6} x - 6 \frac{1}{3}$

The equation of the line is $y = \frac{5}{6} x - 6 \frac{1}{3}$ [Ans]