# How do you write an equation in standard form given a line that passes through (-9,-2) and (7,9)?

May 30, 2015

The easiest way to solve this requirement is to:

• Step 1: write the equation in point-slope form
• Step 2: convert the point-slope form into standard form

Step1: point-slope form
Given the two points $\left(- 9 , - 2\right)$ and $\left(7 , 9\right)$
the slope is given as
$\textcolor{w h i t e}{\text{XXXXX}}$$m = \frac{\Delta y}{\Delta x} = \frac{9 - \left(- 2\right)}{7 - \left(- 9\right)} = \frac{11}{16}$
Using this slope and the point $\left(7 , 9\right)$ (we could use either given point)
the point-slope form is
$\textcolor{w h i t e}{\text{XXXXX}}$$\left(y - 9\right) = \frac{11}{16} \left(x - 7\right)$

Step 2: Convert to standard form
Standard form is (normally) expressed as
$\textcolor{w h i t e}{\text{XXXXX}}$$A x + B y = C$ with $A \ge 0 \mathmr{and} A \epsilon \mathbb{Z}$
Starting with
$\textcolor{w h i t e}{\text{XXXXX}}$$\left(y - 9\right) = \frac{11}{16} \left(x - 7\right)$
we can write
$\textcolor{w h i t e}{\text{XXXXX}}$$16 \left(y - 9\right) = 11 \left(x - 7\right)$

$\textcolor{w h i t e}{\text{XXXXX}}$$16 y - 144 = 11 x - 77$

$11 x - 16 y = - 67$$\textcolor{w h i t e}{\text{XXXXX}}$(standard form)