Question 82888
To graph {{{y=3x}}} we simply need two points to draw a line through. So lets find the first point:


Let x=0

{{{y=3(0)}}} Plug in x=0


{{{y=0}}} Multiply


So we have a point (0,0)

{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  blue( circle( 0,0, .15, 1.5 )),
  blue( circle( 0,0, .1, 1.5 ) )
)}}} Here is the point (0,0) plotted on a coordinate system


Now lets find the second point:

Let x=1

{{{y=3(1)}}} Plug in x=6


{{{y=3}}} Multiply



So we have a point (1,3). Add this to our graph

{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  blue( circle( 1,3, .15, 1.5 )),
  blue( circle( 1,3, .1, 1.5 ) ),
  blue( circle( 0,0, .15, 1.5 )),
  blue( circle( 0,0, .1, 1.5 ) )
)}}} Here are the points (0,0) and (1,3) plotted on a coordinate system

Now draw a straight line through these points


{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  line(-3,-9,3,9),
  blue( circle( 1,3, .15, 1.5 )),
  blue( circle( 1,3, .1, 1.5 ) ),
  blue( circle( 0,0, .15, 1.5 )),
  blue( circle( 0,0, .1, 1.5 ) )
)}}} Graph of {{{y=3x}}} with the points (0,0) and (1,3)


-------------------------------------------------------------------------


To graph {{{y=x-1}}} we simply need two points to draw a line through. So lets find the first point:


Let x=0

{{{y=(0)-1}}} Plug in x=0


{{{y=-1}}} Subtract


So we have a point (0,-1)

{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  blue( circle( 0,-1, .15, 1.5 )),
  blue( circle( 0,-1, .1, 1.5 ) )
)}}} Here is the point (0,-1) plotted on a coordinate system


Now lets find the second point:

Let x=1

{{{y=(1)-1}}} Plug in x=6


{{{y=0}}} Multiply



So we have a point (1,0). Add this to our graph

{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  blue( circle( 1,0, .15, 1.5 )),
  blue( circle( 1,0, .1, 1.5 ) ),
  blue( circle( 0,-1, .15, 1.5 )),
  blue( circle( 0,-1, .1, 1.5 ) )
)-1}}} Here are the points (0,-1) and (1,0) plotted on a coordinate system

Now draw a straight line through these points


{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  line(-10,-11,10,9),
  blue( circle( 1,0, .15, 1.5 )),
  blue( circle( 1,0, .1, 1.5 ) ),
  blue( circle( 0,-1, .15, 1.5 )),
  blue( circle( 0,-1, .1, 1.5 ) )
)}}} Graph of {{{y=x-1}}} with the points (0,-1) and (1,0)


-------------------------------------------------------------------------

To graph {{{y=2x-1}}} we simply need two points to draw a line through. So lets find the first point:


Let x=0

{{{y=2(0)-1}}} Plug in x=0


{{{y=-1}}} Multiply and subtract


So we have a point (0,-1)

{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  blue( circle( 0,-1, .15, 1.5 )),
  blue( circle( 0,-1, .1, 1.5 ) )
)}}} Here is the point (0,0) plotted on a coordinate system


Now lets find the second point:

Let x=1

{{{y=2(1)-1}}} Plug in x=6


{{{y=2-1}}} Multiply


{{{y=1}}} Subtract



So we have a point (1,1). Add this to our graph

{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  blue( circle( 1,1, .15, 1.5 )),
  blue( circle( 1,1, .1, 1.5 ) ),
  blue( circle( 0,-1, .15, 1.5 )),
  blue( circle( 0,-1, .1, 1.5 ) )
)-1}}} Here are the points (0,-1) and (1,1) plotted on a coordinate system

Now draw a straight line through these points


{{{drawing( 300, 300, -5, 5, -5, 5,
  grid( 1 ),
  line(-10,-21,10,19),
  blue( circle( 1,1, .15, 1.5 )),
  blue( circle( 1,1, .1, 1.5 ) ),
  blue( circle( 0,-1, .15, 1.5 )),
  blue( circle( 0,-1, .1, 1.5 ) )
)}}} Graph of {{{y=2x-1}}} with the points (0,-1) and (1,1)