Question 82928
{{{6x-7y=8}}} Start with the given equation


{{{-7y=8-6x}}} Subtract 6x from both sides


{{{y=(8-6x)/-7}}} Divide both sides by -7


{{{y=(6/7)x-8/7}}} Break up the fraction and rearrange the terms so the x term is first. Now it is in {{{y=mx+b}}} form where {{{m=6/7}}} and {{{b=-8/7}}}. So to graph this line, lets plug in point x=-8


Let x=-8

{{{y=(6/7)(-8)-8/7}}} Plug in x=-8


{{{y=-48/7-8/7}}} Multiply


{{{y=-56/7}}} Combine the fractions


{{{y=-8}}} Reduce

So we have a point (-8,-8)

{{{drawing( 300, 300, -10, 10, -10, 10,
  grid( 1 ),
  blue( circle( -8,-8, .15, 1.5 )),
  blue( circle( -8,-8, .2, 1.5 ) )
)}}} Here is the point (-8,-8) plotted on a coordinate system


Let x=6

{{{y=(6/7)(6)-8/7}}} Plug in x=6


{{{y=36/7-8/7}}} Multiply


{{{y=28/7}}} Combine the fractions


{{{y=4}}} Reduce

So we have a point (6,4). Add this to our graph

{{{drawing( 300, 300, -10, 10, -10, 10,
  grid( 1 ),
  blue( circle( 6,4, .15, 1.5 )),
  blue( circle( 6,4, .2, 1.5 ) ),
  blue( circle( -8,-8, .15, 1.5 )),
  blue( circle( -8,-8, .2, 1.5 ) )
)}}} Here are the points (6,4) and (-8,-8) plotted on a coordinate system

Now draw a straight line through these points


{{{drawing( 300, 300, -10, 10, -10, 10,
  grid( 1 ),
  line(-36,-32,20,16),
  blue( circle( 6,4, .15, 1.5 )),
  blue( circle( 6,4, .2, 1.5 ) ),
  blue( circle( -8,-8, .15, 1.5 )),
  blue( circle( -8,-8, .2, 1.5 ) )
)}}} Graph of {{{y=(6/7)x-8/7}}} with the points (6,4) and (-8,-8)