Q: What equation has a region with a straight-line boundary?

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y - x + 1 have no boundary as we don't know what x and y are. I shouldn't say "no boundary", it's more of that the boundary is not defined.

The intersect

The boundary of an inequality is formed by the corresponding equation.

its a straightline. All points y where x is equal to 100. So its a vertical line covering the whole real line in the Y plane through x = 100

Boundary conditions allow to determine constants involved in the equation. They are basically the same thing as initial conditions in Newton's mechanics (actually they are initial conditions).

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a boundary

y - x + 1 have no boundary as we don't know what x and y are. I shouldn't say "no boundary", it's more of that the boundary is not defined.

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The intersect

Boundary.

The boundary of an inequality is formed by the corresponding equation.