Jan 2, 2018

$y = \frac{1}{10} x - \frac{13}{5}$

#### Explanation:

First find the gradient by doing change in y/change in x such as...

m(gradient)= $\frac{- 3 - \left(- 4\right)}{- 4 - \left(- 14\right)}$
=$\frac{1}{10}$

equation is y=$\frac{1}{10} x + b$

to find b you will need to substitute one of the points to the equation and solve for b
such as...

(-4,-3)
(x,y)

$= - 3 = \frac{1}{10} \left(- 4\right) + b$
$= - 3 = - \frac{2}{5} + b$
$= - \frac{13}{5} = b$

equation is $y = \frac{1}{10} x - \frac{13}{5}$

you can also use $y - y 1 = m \left(x - x 1\right)$(point-slope formula).

Jan 2, 2018

$y = \setminus \frac{1}{10} x - \setminus \frac{13}{5}$

#### Explanation:

Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ you have to use this formula here:
$\setminus \frac{y - {y}_{1}}{{y}_{2} - {y}_{1}} = \setminus \frac{x - {x}_{1}}{{x}_{2} - {x}_{1}}$

Let's substitute:
$\setminus \frac{y - \left(- 4\right)}{- 3 - \left(- 4\right)} = \setminus \frac{x - \left(- 14\right)}{- 4 - \left(- 14\right)}$

$\setminus \frac{y + 4}{- 3 + 4} = \setminus \frac{x + 14}{- 4 + 14}$

$\setminus \frac{y + 4}{1} = \setminus \frac{x + 14}{10}$

$y + 4 = \setminus \frac{x + 14}{10}$

$10 \left(y + 4\right) = x + 14$

$10 y + 40 = x + 14$

$10 y = x + 14 - 40$

$10 y = x - 26$

$y = \setminus \frac{1}{10} x - \setminus \frac{26}{10}$

The final result:
$y = \setminus \frac{1}{10} x - \setminus \frac{13}{5}$