# How do you write y+4=2/3(x+7) in standard form?

Jan 31, 2017

$2 x - 3 y = - 2$

#### Explanation:

A linear equation with an $x , y$ and number term represents a straight line.
It can be written in different forms:

General form: $a x + b y + c = 0 \text{ } \leftarrow$ no fractions

Standard form: $a x + b y = c \text{ } \leftarrow$ no fractions

Slope/intercept form: $y = m x + c \text{ } \leftarrow$ may have fractions

$y + 4 = \frac{2}{3} \left(x + 7\right) \text{ "larr" } \times 3$ to get rid of the denominator

$3 y + 12 = 2 \left(x + 7\right) \text{ } \leftarrow$ multiply the bracket by 2

$3 y + 12 = 2 x + 14 \text{ } \leftarrow$ re-arrange the terms

The $x$ term is usually positive

$12 - 14 = 2 x - 3 y$

$2 x - 3 y = - 2$