AI Tutor
Every time your phone alerts you that you entered a delivery zone, it uses a half-plane — a shaded region of a coordinate grid bordered by a straight line.
If someone hands you a graph with a boundary line and a shaded region, how do you work backward to find the exact algebraic inequality?

The Two-Step Blueprint

Writing an inequality from a graph requires just two jobs: finding the equation of the boundary line, and then picking the correct inequality symbol.
The boundary line divides the plane into two halves, and its line style tells you whether boundary points count as solutions.
How do we pinpoint the exact equation of that boundary line before dealing with the shading?

Finding the Boundary Line

Treat the boundary line as a regular linear equation in slope-intercept form: y=mx+by = mx + b.
The y-intercept bb is where the line crosses the vertical yy-axis, while the slope m=riserunm = \frac{\text{rise}}{\text{run}} measures vertical change over horizontal change between any two points.
Once you have y=mx+by = mx + b, how do you know which of the four inequality symbols (<<, >>, ≤\le, or ≥\ge) replaces the equal sign?

Choosing the Symbol with a Test Point