Question
When a point on a graph falls on the boundary line is it always a solution or not a solution
Answers
GPT-4o mini
Whether a point on the boundary line of a graph is considered a solution depends on the type of inequality you are dealing with:
1. **Linear inequalities (less than or greater than)**: If the inequality is strict (e.g., \(y < mx + b\) or \(y > mx + b\)), points on the boundary line (where \(y = mx + b\)) are **not** considered solutions.
2. **Linear inequalities (less than or equal to or greater than or equal to)**: If the inequality includes equal signs (e.g., \(y \leq mx + b\) or \(y \geq mx + b\)), then points on the boundary line **are** considered solutions since the inequality includes the boundary.
In summary, whether a point on the boundary line is a solution depends on whether the inequality is strict or includes equality.
1. **Linear inequalities (less than or greater than)**: If the inequality is strict (e.g., \(y < mx + b\) or \(y > mx + b\)), points on the boundary line (where \(y = mx + b\)) are **not** considered solutions.
2. **Linear inequalities (less than or equal to or greater than or equal to)**: If the inequality includes equal signs (e.g., \(y \leq mx + b\) or \(y \geq mx + b\)), then points on the boundary line **are** considered solutions since the inequality includes the boundary.
In summary, whether a point on the boundary line is a solution depends on whether the inequality is strict or includes equality.