```Question 82970

{{{-y=4-2x}}} Subtract 2x from both sides

{{{y=(4-2x)/-1}}} Divide both sides by -1

{{{y=2x-4}}} Break up the fraction and rearrange the terms so the x term is first. Now it is in {{{y=mx+b}}} form where {{{m=2}}} and {{{b=-4}}}. So to graph this line, lets plug in point x=2 (any x value will work)

Let x=2

{{{y=2(2)-4}}} Plug in x=2

{{{y=4-4}}} Multiply

{{{y=0}}} Subtract

So we have a point (2,0)

{{{drawing( 300, 300, -5, 5, -5, 5,
grid( 1 ),
blue( circle( 2,0, .15, 1.5 )),
blue( circle( 2,0, .1, 1.5 ) )
)}}} Here is the point (2,0) plotted on a coordinate system

Let x=3

{{{y=2(3)-4}}} Plug in x=3

{{{y=6-4}}} Multiply

{{{y=2}}} Subtract

So we have a point (3,2). Add this to our graph

{{{drawing( 300, 300, -5, 5, -5, 5,
grid( 1 ),
blue( circle( 3,2, .15, 1.5 )),
blue( circle( 3,2, .1, 1.5 ) ),
blue( circle( 2,0, .15, 1.5 )),
blue( circle( 2,0, .1, 1.5 ) )
)}}} Here are the points (2,0) and (3,2) plotted on a coordinate system

Now draw a straight line through these points

{{{drawing( 300, 300, -5, 5, -5, 5,
grid( 1 ),
line(-10,-24,10,16),
blue( circle( 3,2, .15, 1.5 )),
blue( circle( 3,2, .1, 1.5 ) ),
blue( circle( 2,0, .15, 1.5 )),
blue( circle( 2,0, .1, 1.5 ) )
)}}} Graph of {{{y=2x-4}}} with the points (2,0) and (3,2)

Another way we could graph {{{y=2x-4}}} is to start with the y-intercept. We know that since {{{b=-4}}} this means the y-intercept is (0,-4). So we have one point (0,-4)

{{{drawing( 300, 300, -5, 5, -5, 5,
grid( 1 ),
blue( circle( 0,-4, .15, 1.5 )),
blue( circle( 0,-4, .1, 1.5 ) )
)}}} Here is the point (0,-4) plotted on a coordinate system

Now since the slope is {{{m=2}}}, which is really {{{m=2/1}}}, it tells us that the next point can be found if we go 2 units up and one unit to the left to find our next point (1,-2)

So we have another point (1,-2)

{{{drawing( 300, 300, -5, 5, -5, 5,
grid( 1 ),
blue( circle( 1,-2, .15, 1.5 )),
blue( circle( 1,-2, .1, 1.5 ) ),
blue( circle( 0,-4, .15, 1.5 )),
blue( circle( 0,-4, .1, 1.5 ) )
)}}} Here are the points (0,-4) and (1,-2) plotted on a coordinate system

Now to make the line, just draw a straight line through the points

{{{drawing( 300, 300, -5, 5, -5, 5,
grid( 1 ),
line(-10,-24,10,16),
blue( circle( 1,-2, .15, 1.5 )),
blue( circle( 1,-2, .1, 1.5 ) ),
blue( circle( 0,-4, .15, 1.5 )),
blue( circle( 0,-4, .1, 1.5 ) )
)}}} Graph of {{{y=2x-4}}} with the points (0,-4) and (1,-2) ```