# How do you write an equation in standard form given point (2,-2) and slope 3?

Jun 14, 2017

$y - 3 x = - 8$

#### Explanation:

Since we are given a point and slope, it's easier to write the equation in the point-slope form, $y - {y}_{1} = m \left(x - {x}_{1}\right)$ and then rewrite it so that it is in the form $A x + B y = C$

Plug in for ${y}_{1}$, ${x}_{1}$, and $m$:

$y - \left(- 2\right) = 3 \left(x - 2\right)$

Distribute:

$y + 2 = 3 x - 6$

Move $3 x$ over to the other side:

$y + 2 - 3 x = 3 x - 6 - 3 x$

$y - 3 x + 2 = - 6$

Move $2$ to the other side:

$y - 3 x + 2 - 2 = - 6 - 2$

$y - 3 x = - 8$

Our equation is now in standard form. Note that $A = 1$ in this case.