How do you graph #-3x=6y-2# using the intercepts?

2 Answers
May 8, 2016

Answer:

Please see below.

Explanation:

Intercepts formed by the line #-3x=6y-2# on #x# axis and #y# axis can be obtained by putting #y=0# and #x=0# respectively in the equation #-3x=6y-2#.

Doing so, intercept on #x# axis is given by #-3x=6*0-2=-2# or #x=2/3#. And intercept on #y# axis is given by #-3*0=6y-2# or #y=1/3#.

Hence, intercept on #x# axis is #2/3# and that on #y# axis is #1/3#. So plotting points #(2/3,0)# and #(0,1/3)# and joining them wil give us the desired graph.

graph{3x+6y-2=0 [-0.2865, 0.9635, -0.1375, 0.4875]}

Additional information - Equation of a line which forms an intercept #a# on #x# axis and #b# on #y# axis is given by #x/a+y/b=1#.

May 8, 2016

Answer:

Mart the points
#color(green)(=>y_("intercept")->(x,y)->(0,1/3)#
#=>color(green)(x_("intercept") ->(x,y)->(2/3,0)#
and draw a straight line through them but extend it to the edges of the graph.

Explanation:

We could if we so chose manipulate the given equation so that we have the standard form of #y=mx + c# and then determine the intercepts, but there is no need to.

#color(green)("Determine x-intercept")#
Using first principle method

Knowing the First principle method comes in handy when doing higher level math.

The #x"-intercept"# is when #color(blue)(y=0)#

So by substitution we have:

#color(brown)(-3x=6y-2" "->" "-3x=6(color(blue)(0))-2)#

#=>-3x=-2#

Multiply both sides by #(-1)#

#=> +3x=+2#

Divide both sides by 3

#3/3x=2/3#

But #3/3=1#

#color(green)(x_("intercept")=2/3) ->(x,y)->(2/3,0)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(green)("Determine y-intercept")#
Using shortcuts method

The #y"-intercept"# is when #x=0#

#-3(0)=6y-2#

#color(green)(=>y=+2/6=1/3)->(x,y)->(0,1/3)#