How do you find the slope that is perpendicular to the line # y = x + 7#?

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Answer 1 · 2018-03-19T19:32:35

See a solution process below:

The equation in the problem is in 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.

#y = color(red)(1)x + color(blue)(7)#

Therefore the slope is: #color(red)(m = 1)#

Let's call the slope of a perpendicular line: #color(blue)(m_p)#

The slope of a line perpendicular to a line with slope #color(red)(m)# is the negative inverse, or:

#color(blue)(m_p) = -1/color(red)(m)#

Substituting the slope for the line in the problem gives:

#color(blue)(m_p) = (-1)/color(red)(1) = -1#