How do you find the slope that is perpendicular to the line #3x + 2y = -6#?

1 Answer
Mar 12, 2017

Answer:

#"perpendicular slope "=2/3#

Explanation:

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#
where m represents the slope and b, the y-intercept.

#"Rearrange " 3x+2y=-6" into this form"#

subtract 3x from both sides.

#cancel(3x)cancel(-3x)+2y=-3x-6#

#rArr2y=-3x-6#

divide both sides by 2

#(cancel(2) y)/cancel(2)=-3/2x-2#

#rArry=-3/2x-2larr" in slope-intercept form"#

#rArr"slope "=-3/2#

The slope perpendicular to this is the #color(blue)"negative reciprocal"# of m

#rArrm_("perpendicular")=-1/(-3/2)=2/3#