# Given two ordered pairs (1,-2) and (3,-8), what is the equation of the line in slope-intercept form?

Nov 26, 2015

$y = - 3 x + 1$

#### Explanation:

The general equation for a line in slope-intercept form is:

$y = m x + b$

where:
y = y-coordinate
m = slope
x = x-coordinate
b = y-intercept

To find the equation, first find the slope. The formula for slope is:

$m = \left({y}_{\text{2"-y_"1")/(x_"2"-x_"1}}\right)$

where:
m = slope
$\left({x}_{\text{1", y_"1}}\right) = \left(1 , - 2\right)$
$\left({x}_{\text{2", y_"2}}\right) = \left(3 , - 8\right)$

$m = \left({y}_{\text{2"-y_"1")/(x_"2"-x_"1}}\right)$

$m = \frac{\left(- 8\right) - \left(- 2\right)}{\left(3\right) - \left(1\right)}$

$m = - \frac{6}{2}$

$m = - 3$

Rewrite the equation:

$y = - 3 x + b$

Now substitute a known point into the equation to solve for $b$:

$y = - 3 x + b$

$\left(- 2\right) = - 3 \left(1\right) + b$

$- 2 = - 3 + b$

$1 = b$

$y = - 3 x + 1$