# How do you write an equation of the line in standard form with m = 4/3 (-2,-6)?

Oct 28, 2015

First write the equation in slope-point form
then convert to standard form, to get
$\textcolor{w h i t e}{\text{XXX}} 4 x - 3 y = 10$

#### Explanation:

Slope-point form:
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$
$\textcolor{w h i t e}{\text{XXXXXXXXX}}$for a line with slope $m$ through the point $\left(\hat{x} , \hat{y}\right)$

For the given data this becomes
[1]$\textcolor{w h i t e}{\text{XXX}} y + 6 = \frac{4}{3} \left(x + 2\right)$

Standard form for a linear equation is
$\textcolor{w h i t e}{\text{XXX}} A x + B y = C$
$\textcolor{w h i t e}{\text{XXXXXXXXX}}$for $A , B , C \in \mathbb{Z}$ and $A \ge 0$

Simplifying [1]
[2]$\textcolor{w h i t e}{\text{XXX}} 3 y + 18 = 4 x + 8$

Subtracting $\left(3 y + 8\right)$ from both sides
[3]$\textcolor{w h i t e}{\text{XXX}} 10 = 4 x - 3 y$

Reversing the sides to get standard form:
[4]$\textcolor{w h i t e}{\text{XXX}} 4 x - 3 y = 10$