What are the x and y intercepts of the linear equation: #-y=(3x+6)-12#?

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Answer 1 · 2018-05-19T03:54:45

y-int = 6
x-int = 2

#-y=(3x+6)-12#

first remove the parentheses:
#-y=3x+6 -12#

combine like terms
#-y=3x-6#

multiply both sides by -1
#(-1)-y=(-1)(3x-6)#

#y=-3x+6#

to find the y-intercept set x = 0

#y=-3(0)+6#

#y=6#

to find the x-intercept set y = 0

#0=-3x+6#

#-6=-3x#

#2 = x# or #x = 2#

graph{y=-3x+6 [-13.71, 14.77, -6.72, 7.52]}

Answer 2 · 2018-05-19T03:57:07

#x-#intercept is #(2,0)#
#y-#intercept is #(0,6)#

#-y =(3x+6)-12#

First let's restate the equation in more common form.

(i) The parentheses are serving on purpose here.

#-y =3x+6-12#

#-y=3x-6#

(ii) Multiply through by #-1#

#y = -3x+6#

Here we have the equation in slope/intercept form: #y=mx+c#

Hence the #y-#intercept is #(0,6)#

The #x-#intercept occurs where #y=0 ->#

#0 = -3x+6#

#3x=6 -> x=2#

#:. # the #x-#intercept is #(2,0)#

These intercepts can be seen on the graph of #y# below.

graph{-y =(3x+6)-12 [-16.03, 16.01, -8, 8.03]}