How do you find the slope and intercept of #-4x+2y=12#?

1 Answer
Alan P.
Apr 10, 2016

Slope: #2#
y-intercept: #6#
(x-intercept: #-3#)

Explanation:

slope
Given an equation in the form #Ax+By=C# the slope is #(-A/B)#
So #-4x+2y=12# has a slope of #-(-4)/2=2#

Alternately, we could convert the given form
into "slope-intercept form": #y=mx+b# with slope #m# and y-intercept #b#
#color(white)("XXX")-4x+2y=12#
#color(white)("XXX")rarr 2y=4x+12#
#color(white)("XXX")rarr y = 2x+6#

y-intercept
If we used the "slope-intercept form" (above) we already have the y-intercept: #6#;
otherwise we can determine the y-intercept by finding the value of #y# when #x=0# in the given equation: #-4x+2y=12#
#color(white)("XXX")-4xx(0)+2y=12#
#color(white)("XXX")rarr y=6#

x-intercept (note sometimes when "the intercept" is asked for, what is meant is only the y-intercept)
The x-intercept can be determined by find the value of #x# when #y=0# in the given equation: #-4x+2y=12#
#color(white)("XXX")-4x+2xx(0)=12#
#color(white)("XXX")rarr x=-3#

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