Question 204539
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Particularly in your situation, you are looking linear equation in the two variables x and y.


Examples: {{{-x[1]+y[1]=1}}} & {{{-x[2]+y[2]=2}}}


Following Slope-Intercept Form, {{{y=mx+b}}}:
{{{y[1]=x[1]+1}}} ---> {{{y[1]=red(1)x[1]+1}}}
{{{y[2]=x[2]+2}}} ---> {{{y[2]=red(1)x[2]+2}}}


*It shows, {{{m[1]=m[2]=1}}} --> the two lines are <font color=blue>PARALLEL</font>


To check,
In Eqn 1, let Fy=0:
{{{-x+0=1}}} ---> {{{x=-1}}}, X-intercept
Let Fx=0:
{{{0+y=1}}} ---> {{{y=1}}}, Y-intercept


In Eqn 2: let Fy=0:
{{{-x+0=2}}} ---> {{{x=-2}}}, X-intercept
Let Fx=0:
{{{0+y=2}}} ---> {{{y=2}}}, Y-intercept
{{{drawing(300,300,-6,6,-6,6,grid(1),graph(300,300,-6,6,-6,6,x+1,x+2),blue(circle(-1,0,.11)),blue(circle(0,1,.11)),blue(circle(-2,0,.11)),blue(circle(0,2,.11)))}}} ---> When you see the Slope (m) of one linear equation equals to the other eqn, they are parallel.


Thank you,
Jojo</font>