# Given the two ordered pairs (1,-2), and (3,-8), how do you write the equation of then line in slope intercept form?

Jul 1, 2015

$y = - 3 x + 1$

#### Explanation:

The slope for a line passing through $\left(1 , - 2\right)$ and $\left(3 , - 8\right)$ is
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{\Delta y}{\Delta x} = \frac{\left(- 8\right) - \left(- 2\right)}{3 - 1} = - 3$

For a general point $\left(x , y\right)$ on this line the slope is
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{y - \left(- 2\right)}{x - 1}$

Since the slope is constant for a straight line
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{y + 2}{x - 1} = - 3$
$\Rightarrow$
$\textcolor{w h i t e}{\text{XXXX}}$$y + 2 = - 3 x + 3$
$\Rightarrow$
$\textcolor{w h i t e}{\text{XXXX}}$$y = - 3 x + 1$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$which is the slope-intercept form
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$with slope $\left(- 3\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$and y-intercept $1$