How do you find the slope of #3x + 2y = -6#?

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Answer 1 · 2017-02-05T10:18:04

See the entire solution process below:

To find the slope we should convert this equation to slope-intercept form. The slope-intercept form of a linear equation is:

#y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

Solving for #y# gives:

#3x + 2y - color(red)(3x) = -6 - color(red)(3x)#

#3x - color(red)(3x) + 2y = - color(red)(3x) - 6#

#0 + 2y = -3x - 6#

#2y = -3x - 6#

#(2y)/color(red)(2) = (-3x - 6)/color(red)(2)#

#(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = (-3x)/color(red)(2) - 6/color(red)(2)#

#y = color(red)(-3/2)x - color(blue)(3)#

With the equation in slope-intercept form we now know the slope is:

#color(red)(m = -3/2)#