Defining a line from an inequality

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So I am currently working on understanding a solution to a complex problem. I am stuck with one of the things that are "logical jumps" that are described.

The author defines a Euclidean plane of $(p, v)$.

Then he states the following inequality which I undestand and agree with:

$P + t V − 4 ≤ a + t b ≤ P + t V$, where $(P, V)$ and $(a, b)$ are points on the plane and $t$ is time.

He then states that the abovementioned inequality defines an infinite strip of slope $(-1/t)$ and horizontal width $4$.

I tried graphing the inequality in Geogebra, but strange things happen and it only seems to work for $t=1$.

I would very much appreciate any help that could conclude in me understanding how the author came up with his conclusion regarding the "infinite strip of..."

Thanks in advance!