# How do you write y-5 = 3/2 (x+4) in standard form?

Sep 13, 2015

$3 x - 2 y = - 22$

#### Explanation:

Standard form for a linear equation is
$\textcolor{w h i t e}{\text{XXXX}} A x + B y = C$
color(white)("XX")"with "A, B, C in ZZ, A>=0

Given
$\textcolor{w h i t e}{\text{XX}} y - 5 = \frac{3}{2} \left(x + 4\right)$
Multiply both sides by $3$ (and simplify the right side)
$\textcolor{w h i t e}{\text{XX}} 2 y - 10 = 3 x + 12$
$\textcolor{w h i t e}{\text{XX}} 2 y = 3 x + 22$
Subtract $3 x$ from both sides
$\textcolor{w h i t e}{\text{XX}} - 3 x + 2 y = 22$
Multiply both sides by $\left(- 1\right)$
$\textcolor{w h i t e}{\text{XX}} 3 x - 2 y = - 22$

Sep 13, 2015

$3 x - 2 y = - 22$=>standard form.

#### Explanation:

The equation of line in the standard form is:

$A x + B y = C$

where A is a positive integer, and B, and C are integers.

So in this case:

$y - 5 = \frac{3}{2} \left(x + 4\right)$ => multiply both sides by 2:

$2 y - 10 = 3 \left(x + 4\right)$ => expand the right side:

$2 y - 10 = 3 x + 12$ => rewrite as:

$3 x + 12 = 2 y - 10$=> subtract 2y from both sides:

$3 x - 2 y + 12 = - 10$=> subtract 12 from both sides:

$3 x - 2 y = - 22$=>standard form.