# How do you find the equation of the line that goes through (-3, 1) and (1, -3)?

Oct 4, 2017

Equation: $x + y + 2 = 0$

#### Explanation:

The two point are $\left(- 3 , 1\right)$ and $\left(1 , - 3\right)$.

You can find the equation by using the point-gradient formula, $y - {y}_{1} = m \left(x - {x}_{1}\right)$.

To do this, we first need to find the gradient of the line. This can be done using the gradient formula:

$\frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}$
$= \frac{1 - \left(- 3\right)}{- 3 - 1}$
$= \frac{4}{-} 4$
$= - 1$

We now have the gradient, represented by $m$ in the point-gradient formula, and can choose any one of the two coordinates given by the question to sub into this formula. Let's go with $\left(- 3 , 1\right)$.

$y - {y}_{1} = m \left(x - {x}_{1}\right)$
$y - 1 = - 1 \left(x - \left(- 3\right)\right)$
y-1=-1(x+3))
$y - 1 = - x - 3$
$\therefore y = - x - 2$

Or, if the question asks for the equation in general form, move all the values to one side so that the coefficient of $x$ is positive and the equation equals to $0$:
$y = - x - 2$
$\therefore x + y + 2 = 0$