Graphing Linear Inequalities Activity

Welcome to Friendly Math 101, where we turn challenging concepts into clear, actionable steps. In this article, we’ll walk through a hands‑on activity that helps students master the art of graphing linear inequalities. By the end, you’ll have a practical lesson plan, ready to use in the classroom or for self‑study.

Understanding Linear Inequalities

On this page, we’ll first define what a linear inequality is and why it matters in algebra and real‑world applications.

Inequalities compare two expressions using symbols such as <, >, ≤, or ≥.
A linear inequality involves a straight line when graphically represented.
Graphing these inequalities helps visualize solution sets and understand relationships between variables.

Step‑by‑Step Activity

In this video, learn how to convert a linear inequality into a graph. Follow the steps below to create an engaging, interactive lesson.

1. Identify the Inequality

Start with a simple inequality, for example: y < 2x + 3. Write it on the board or display it on a screen.

2. Convert to Equality for the Boundary Line

Replace the inequality symbol with an equals sign to find the boundary line: y = 2x + 3. This line will be dashed if the original inequality was strict (< or >).

3. Plot the Boundary Line

Choose two easy x‑values (e.g., x = 0 and x = 1).
Calculate the corresponding y‑values: for x = 0, y = 3; for x = 1, y = 5.
Plot the points (0, 3) and (1, 5) and draw a dashed line through them.

4. Test a Point Outside the Boundary

Pick a test point not on the line, such as (0, 0). Substitute it into the original inequality: 0 < 2(0) + 3 → 0 < 3, which is true. Shade the region that includes this test point.