why is it that in a linear inequality, each point on a dashed boundary line is not a solution?

Answer 1

suppose you have the graph of
y > 2x + 5

the graph would consist of all the points above the line y = 2x + 5 , but exclude all the points which lie on the line itself

The equation acts like a boundary, but the points on the equation are not part of the region.

to show that the line is only the boundary, we draw the line as a dotted line, if the points are included we make it a solid line

if you want all the points above the line and all the points which lie on the line we used the notation

y ≥ 2x + 5

This is a universally accepted notation.

Answer 2

thanks