# How do you write an equation of the line in standard form that is Parallel to 5y-4x=15 and through (10,6)?

Oct 19, 2015

$4 x - 5 y = 10$

#### Explanation:

$5 y - 4 x = 15$ has a slope of $\frac{4}{5}$

The slope-point form of a linear equation is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$
$\textcolor{w h i t e}{\text{XXXXXXX}}$where $m$ is the slope and $\left(\hat{x} , \hat{y}\right)$ is a point

For this example we have
$\textcolor{w h i t e}{\text{XXX}} \left(y - 6\right) = \frac{4}{5} \left(x - 10\right)$

Simplifying:
$\textcolor{w h i t e}{\text{XXX}} y = \frac{4}{5} x - 8 + 6$

$\textcolor{w h i t e}{\text{XXX}} 5 y = 4 x - 10$

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

Converting to standard form:
$\textcolor{w h i t e}{\text{XXX}} 4 x - 5 y = 10$