What is the slope of the line perpendicular to # y=-5/3-6 #?

2 Answers
Jan 13, 2018

Answer:

As asked #y=-5/3-6=-23/6# is a horizontal line; any line perpendicular to it would be vertical and thus have an undefined slope.
If the intended equation was #y=-5/3color(blue)x-6#
see below.

Explanation:

Any equation in the form #y=color(green)mx+b# is in slope-intercept form with a slope of #color(green)m#

If a line has a slope of #color(green)m#
then all lines perpendicular to it have a slope of #-(1/color(green)m)#

If the equation was intended to be
#color(white)("XXX")y=color(green)(-5/3)x-6#
then all lines perpendicular to it will have a slope:
#color(white)("XXX")-(1/(color(green)(-5/3)))=color(magenta)(3/5)#

Jan 13, 2018

Answer:

#"slope "=3/5#

Explanation:

#"assuming "y=-5/3x-6" is meant"#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#y=-5/3x-6" is in this form with "m=-5/3#

#"given a line with slope m then the slope of a line"#
#"perpendicular to it is"#

#•color(white)(x)m_(color(red)"perpendicular")=-1/m#

#rArrm_(color(red)"perpendicular")=-1/(-5/3)=3/5#