# What is the equation of the line with slope  m=5/9  that passes through  (-2,-4) ?

Dec 15, 2015

$\left(y + 4\right) = \frac{5}{9} \left(x + 2\right)$ [in slope-point form]
or
$5 x - 9 y = 26$ [in standard form]

#### Explanation:

The slope-point form for a line with slope $m$ through a point $\left(\overline{x} , \overline{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \overline{y}\right) = m \left(x - \overline{x}\right)$

Replacing the general slope and point coordinates with the given values: $m = \frac{5}{9}$ and $\left(\overline{x} , \overline{y}\right) = \left(- 2 , - 4\right)$
we get
$\textcolor{w h i t e}{\text{XXX}} \left(y - \left(- 4\right)\right) = \frac{5}{9} \left(x - \left(- 2\right)\right)$
or
$\textcolor{w h i t e}{\text{XXX}} \left(y + 4\right) = \frac{5}{9} \left(x + 2\right)$

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If you want this in "standard form"
$\textcolor{w h i t e}{\text{XXX}} A x + B y = C$ with A,B,C in ZZ; A>=0

Multiply both sides by $9$
$\textcolor{w h i t e}{\text{XXX}} 9 y + 36 = 5 x + 10$

Subtract $\left(9 y + 10\right)$ from both sides
$\textcolor{w h i t e}{\text{XXX}} 26 = 5 x - 9 y$

Switch sides:
$\textcolor{w h i t e}{\text{XXX}} 5 x - 9 y = 26$