How do you find the slope that is perpendicular to the line #x + y = -3#?

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Answer 1 · 2017-01-25T23:24:30

See the entire solution process below:

First, we need to transform this equation to the slope-intercept form by solving for #y#.

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.

#x + y = -3#

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

#0 + y = -x - 3#

#y = color(red)(-1)x - color(blue)(3)#

Therefore the slope of this line is #-1#.

A line perpendicular to the line in the problem with have a slope which is the negative inverse of the slope of given line or #-1/m#

Substituting the slope we obtained of #-1# for #m# gives:

#-1/-1 = 1#

The slope of a perpendicular line will have a slope of #1#