How do you write an equation in standard form given (-3, -3), (7,2)?

Jan 27, 2016

$x - 2 y = 3$

Explanation:

Just so we know what our target is:
Standard form for a linear equation is
$\textcolor{w h i t e}{\text{XXX}} A x + B y = C$

Step 1: write the equation in slope-point form

slope: $m = \frac{\Delta y}{\Delta x} = \frac{2 - \left(- 3\right)}{7 - \left(- 3\right)} = \frac{5}{10} = \frac{1}{2}$

slope point form with slope $m$ through a point $\left(\overline{x} , \overline{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \overline{y}\right) = m \left(x - \overline{x}\right)$
Using the above slope and $\left(- 3 , - 3\right)$ for $\left(\overline{x} , \overline{y}\right)$
$\textcolor{w h i t e}{\text{XXX}} y + 3 = \frac{1}{2} \left(x + 3\right)$

Step 2: convert from slope-point to standard form

$y + 3 = \frac{1}{2} \left(x + 3\right)$

$\rightarrow 2 y + 6 = x + 3$

$\rightarrow x - 2 y = 3$$\textcolor{w h i t e}{\text{XXX}}$or if you want to be picky: $1 x + \left(- 2\right) y = 3$