# How do you write an equation in standard form given that the line passes through (-1, -3) and (2, 1)?

Jun 7, 2015

Using this formula with the given points:
$\frac{x - {x}_{0}}{{x}_{1} - {x}_{0}} = \frac{y - {y}_{0}}{{y}_{1} - {y}_{0}}$

The points are:

• $A \left({x}_{0} , {y}_{0}\right) \to A \left(- 1 , - 3\right)$
• $B \left({x}_{1} , {y}_{1}\right) \to B \left(2 , 1\right)$

So the equation of the line passing through A and B becomes:
$\frac{x - \left(- 1\right)}{2 - \left(- 1\right)} = \frac{y - \left(- 3\right)}{1 - \left(- 3\right)}$

$\frac{x + 1}{2 + 1} = \frac{y + 3}{4}$

$\frac{x + 1}{3} = \frac{y + 3}{4}$

Now we must bring the equation in a "standard form" that means an equation similar to $a x + b y + c = 0$

$4 \cdot \left(x + 1\right) = \left(y + 3\right) \cdot 3$

$4 x + 4 = 3 y + 9$

$4 x - 3 y - 5 = 0$

graph{4x-3y-5=0 [-3, 3,-3,3]}