How does the dotted or solid line help determine if a point is a solution?

Answer 1

I will assume you are talking about graphing linear inequalities.

In that case, we use a dotted line for "strict" inequalities (< or >) and a solid line otherwise (≤ or ≥). This convention helps because points that lie on a solid line in the graph ARE solutions to the inequality, whereas points lying on a dotted line are NOT solutions.

For example, the point (2,4) lies on the line y = 2x. If the inequality was y ≥ 2x , then the point (2,4) would lie on a SOLID line and it WOULD be a solution. But, if instead the inequality was y > 2x , then the point (2,4) would lie on the dashed line and would NOT be a solution.