# What is the equation of the line between (-1,14) and (14,4)?

##### 1 Answer
Nov 21, 2015

$2 x + 3 y = 40$

#### Explanation:

Given the points $\left(- 1 , 14\right)$ and $\left(14 , 4\right)$
the slope is
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\Delta y}{\Delta x} = \frac{14 - 4}{- 1 - 14} = \frac{10}{- 15} = - \frac{2}{3}$

The slope-point form of the equation for a line with slope $m$ through a point $\left(\hat{x} , \hat{y}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

Arbitrarily choosing $\left(\hat{x} , \hat{y}\right) = \left(14 , 4\right)$ [note that either point would work]:
$\textcolor{w h i t e}{\text{XXX}} \left(y - 4\right) = - \frac{2}{3} \left(x - 14\right)$
and this is one possible solution to the question asked.

However let's put it into standard form ($A x + B y = C$)

$\textcolor{w h i t e}{\text{XXX}} 3 \left(y - 4\right) = - 2 \left(x - 14\right)$

$\textcolor{w h i t e}{\text{XXX}} 3 y - 12 = - 2 x + 28$

$\textcolor{w h i t e}{\text{XXX}} 2 x + 3 y = 40$