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

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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:

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

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

Solving for $y$ $y$ gives:

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

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

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

$2 y = - 3 x - 6$ $2y = -3x - 6$

$\frac{2 y}{2} = \frac{- 3 x - 6}{2}$ $(2y)/color(red)(2) = (-3x - 6)/color(red)(2)$

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

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

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

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

How do you find the slope of 3x + 2y = -63x+2y=−63x + 2y = -6?