What is the slope of the line perpendicular to # y=-13/2x-5 #?

1 Answer
Mar 10, 2018

Answer:

See a solution process below:

Explanation:

The equation for the line 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)(-13/2)x - color(blue)(5)#

Therefore the slope of this line is: #color(red)(m = -13/2)#

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)(-13/2) = 2/13#