Why is the graph of $x-1>y$ like this?

Question

Why is the graph of $x-1>y$ like this? I cannot get it intuitively. Can someone help? Thanks.

Answer 1

Think in terms of horizontal slices and specific values of $y$. When $y$ is specifically equal to $0$ the inequality becomes $x-1>0$ or rearranged, $x>1$. So, think of graphing $x>1$ on the number line.

Do the same for when $y=1$ this becomes $x-1>1$ or rearranged $x>2$.

Imagine doing this for "many" such values of $y$ and coming up with "many" stacked inequalities on the numberline.

Now, make sure that each horizontal slice is at the height corresponding to it's respective $y$-value