# How do you write the equation in slope intercept form given (2,5) and (7,-3)?

May 16, 2016

The slope-intercept form of the equation of the line is
$y = - \frac{8}{5} x + \frac{25}{5}$

#### Explanation:

The formula for the slope of a line based upon two coordinate points is

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the coordinate points $\left(2 , 5\right) \mathmr{and} \left(7 , - 3\right)$
${x}_{1} = 2$
${x}_{2} = 7$
${y}_{1} = 5$
${y}_{2} = - 3$

$m = \frac{- 3 - 5}{7 - 2}$

$m = - \frac{8}{5}$

The slope is $m = - \frac{8}{5}$

The point slope formula would be written as
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$m = - \frac{8}{5}$
${x}_{1} = 2$
${y}_{1} = 5$

$y - 5 = - \frac{8}{5} \left(x - 2\right)$

$y - 5 = - \frac{8}{5} x + \frac{16}{5}$

$y \cancel{- 5} \cancel{+ 5} = - \frac{8}{5} x + \frac{16}{5} + 5$

$y = - \frac{8}{5} x + \frac{16}{5} + \frac{25}{5}$

The slope-intercept form of the equation of the line is
$y = - \frac{8}{5} x + \frac{25}{5}$

The standard form would be
$5 y = - 8 x + 25$