# What is the equation of the line between (-18,14) and (19,24)?

Feb 25, 2016

$y = \frac{10}{37} x - \frac{806}{37}$
or
$37 y = 10 x - 806$

#### Explanation:

The formula for slope is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the points (-18,14) and (19,24) where
${x}_{1} = - 18$
${y}_{1} = 14$
${x}_{2} = 19$
${y}_{2} = 24$

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

m =(24 - 14)/(19-(-18)

$m = \frac{10}{37}$

To determine the equation of the line we can use the point slope formula and plug in the values given in the question.

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

$m = \frac{10}{37}$
${x}_{1} = - 18$
${y}_{1} = 14$

$\left(y - \left(- 18\right)\right) = \frac{10}{37}$(x - 14)#

$y + 18 = \frac{10}{37} x - \frac{140}{37}$

$y + 18 - 18 = \frac{10}{37} x - \frac{140}{37} - 18$

$y = \frac{10}{37} x - \frac{140}{37} - \frac{666}{37}$

$y = \frac{10}{37} x - \frac{806}{37}$

$\left(y = \frac{10}{37} x - \frac{806}{37}\right) x 37$

$37 y = 10 x - 806$