What is this graph ?

The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
[tex]x-y=1[/tex] subtract x from both sides
[tex]-y=-x+1[/tex] change the signs
[tex]y=x-1[/tex]
It's a linear function.
We need only two points to plotting a graph.
We choose any three values of x and calculate y.
[tex]for\ x=0\to y=0-1=-1\to(0,\ -1)\\for\ x=1\to y=1-1=0\to(1,\ 0)\\for\ x=2\to y=2-1=1\to(2,\ 1)[/tex]