How do you find the slope and intercept to graph #3x+4y=-12#?

1 Answer
Mar 28, 2018

#y = -(3)/(4)x - 3#

The slope is #-3/4#

The y-intercept is at #(0,-3)#

Explanation:

The best way to find the slope and the y-intercept of the given line is to re-write the equation in the slope-intercept form.
That way, you can read the slope and the y-intercept directly from the equation.

The slope-intercept form of an equation is
#y = mx + b#
where #m# is the slope and #b# is the y-intercept.

Rewrite the equation in the slope-intercept form

Given #3x+4y=−12#    Solve for #y#

1) Subtract #3x# from both sides to isolate the #4y# term
After you subtract, you will get this:
#4y = - 3x - 12#

2) Divide all the terms on both sides by #4# to isolate #y#
#y = -(3)/(4)x - 3#

This equation tells you that the slope is #-(3)/(4)#, and that the y-intercept us at #(0,-3)#

You can click here to see the graph of this line
https://www.google.com/search?source=hp&ei=eOO7WuTpMYKL5wK8qY6ADw&q=y+%3D+-%283%2F4%29x+-+3&oq=y+%3D+-%283%2F4%29x+-+3&gs_l=psy-ab.12...1454.13188.0.16952.16.15.0.0.0.0.156.1364.9j5.14.0....0...1.1.64.psy-ab..2.4.478.0..0j0i131k1.0.sih2wBD0tnI

Or you can use the Mathway graphing tool to see this line
https://www.mathway.com/PreAlgebra?problem=eT0oMykvKDQpeC0z
(Change the web site's slope of #3/4# into your wanted slope of #-3/4# )