# How do you write the equation of the line that passes through (-3, 3) and (2,-7)?

Aug 4, 2017

$y = - 2 x - 3$

#### Explanation:

The gradient/intercept form of a linear equation is:

$y = m x + c$

We need to solve for the two unknowns $m$ and $c$ to find the equation.

First, solve for the gradient, $m$:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 7 - 3}{2 - \left(- 3\right)} = - 2$

Substitute this value into the gradient/intercept form:

$y = - 2 x + c$

Now substitute in any point on the line to solve for $c$:

$\left(- 3 , 3\right)$:

$3 = - 2 \left(- 3\right) + c \Rightarrow 3 = 6 + c \Rightarrow c = - 3$

$c$ is the y-intercept.

Inserting $c$ and $m$ into the original equation gives the answer:

$\therefore y = m x + c = - 2 x - 3$