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

Question

Eva Adamson · Accepted Answer

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#

Abigail Allen · Answer

undefined To find the slope that is perpendicular to the line $ y = x + 7 $, you first need to determine the slope of the given line. In the equation $ y = mx + b $, where $ m $ represents the slope, the slope of the line $ y = x + 7 $ is $ m = 1 $.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.

So, the slope perpendicular to $ m = 1 $ would be $ m = -\frac{1}{1} $ or simply $ m = -1 $.