# How do you write an equation going through points (-5, 1) (0, -2)?

May 31, 2016

The standard form of the equation would be
$5 y + 3 x = - 10$

#### 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 $\left(- 5 , 1\right) \mathmr{and} \left(0 , - 2\right)$
${x}_{1} = - 5$
${x}_{2} = 0$
${y}_{1} = 1$
${y}_{2} = - 2$

$m = \frac{- 2 - 1}{0 - \left(- 5\right)}$

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

The slope is $m = - \frac{3}{5}$

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

$m = - \frac{3}{5}$
${x}_{1} = - 5$
${y}_{1} = 1$

$y - 1 = - \frac{3}{5} \left(x - \left(- 5\right)\right)$

$y - 1 = - \frac{3}{5} x - 3$

$y \cancel{- 1} \cancel{+ 1} = - \frac{3}{5} x - 3 + 1$

$y = - \frac{3}{5} x - 2$

The slope-intercept form of the equation of the line is
$y = - \frac{3}{5} x - 2$

$\left(5\right) y = \left(- \frac{3}{5} x - 2\right) \left(5\right)$

$5 y = - 3 x - 10$

$5 y + 3 x = \cancel{- 3 x} \cancel{+ 3 x} - 10$

The standard form of the equation would be
$5 y + 3 x = - 10$