What is the slope and y-intercept of the line 2x - 3y = -18?

1 Answer
Jul 29, 2015

Answer:

slope #=2/3#
and\y-intercept #= 6#

Explanation:

Slope
For an equation in the form:
#color(white)("XXXX")##Ax+By=C#
the slope is
#color(white)("XXXX")##m = -A/B#
for the given equation #2x-3x=-12# this becomes
#color(white)("XXXX")##m = 2/3#

Alternatively we could rewrite the given equation #2x-3y =-18#
into "slope intercept" form:
#color(white)("XXXX")##y = mx+b#
#color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")#where #m# is the slope and #b# is the y-intercept
#color(white)("XXXX")#2x-3y = -18#

#rarr##color(white)("XXXX")##-3y = -2x-18#

#rarr##color(white)("XXXX")##y = 2/3x +6#

y-intercept
If you rewrote the equation in "slope intercept form" (see above)
the slope can be read directly from the equation as
#color(white)("XXXX")##m = 6#

Otherwise
note that the y-intercept is the value of #y# when #x=0# in the equation:
#color(white)("XXXX")##2(0)-3y = -18#
#rarr##color(white)("XXXX")##y = 6#