How do you find the slope that is perpendicular to the line #3x + 2y = -6#?
1 Answer
Mar 12, 2017
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#