# What is the slope of a line parallel to 3x+4y=12?

##### 1 Answer
Sep 18, 2014

In this problem we must first find the slope of the given line. Also note that parallel lines have the same slope.

We have 2 options:

1) Manipulate this equation from standard form to slope intercept form, $y = m x + b$, where $m$ is the slope.

2) The slope can be found using the following expression, $- \frac{A}{B}$, when the equation is standard form.

OPTION 1:

$3 x + 4 y = 12$

$4 y = 12 - 3 x$

$\frac{4 y}{4} = \frac{12}{4} - \frac{3 x}{4}$

$y = 3 - \frac{3 x}{4}$

$y = - \frac{3}{4} x + 3 \to s l o p e = - \frac{3}{4}$

OPTION 2:

$A x + B y = C$

$3 x + 4 y = 12$

$s l o p e = - \frac{A}{B} = - \frac{3}{4}$

A line parallel to $3 x + 4 y = 12$ must have a slope of $- \frac{3}{4}$.