Create at least two visual representations (graphs, charts, diagrams) that illustrate key concepts from the unit.
- Provide a brief explanation for each visual, describing what it shows and its significance.
in the Solving Equations and Inequalities subject

### 1. **Graph of Linear Equations**

**Visual Representation:**
- A Cartesian plane showing a linear equation such as \( y = 2x + 3 \), where the line crosses the y-axis at \( y = 3 \) and has a slope of 2. The x-axis and y-axis are labeled, and key points like the y-intercept and a few points on the line are marked.

**Explanation:**
This graph represents the solution set of a linear equation \( y = 2x + 3 \). It shows how each value of \( x \) corresponds to a unique value of \( y \). The slope of 2 indicates that for every increase of 1 unit in \( x \), \( y \) increases by 2 units. The y-intercept at \( (0, 3) \) is the point where the line crosses the y-axis. Linear equations like this one have a consistent rate of change, which makes them a foundational concept in algebra.

**Significance:**
Understanding the graph of a linear equation is crucial for interpreting relationships between variables in real-life situations, such as predicting trends, solving problems involving rates, and more.

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### 2. **Number Line Representation of Inequalities**

**Visual Representation:**
- A number line representing the inequality \( x \geq 2 \). The number 2 is highlighted with a filled circle (indicating that 2 is included), and the area to the right of 2 is shaded to show all numbers greater than or equal to 2.

**Explanation:**
This diagram visually represents the solution set of the inequality \( x \geq 2 \). The filled circle at 2 indicates that 2 is included in the solution, while the shaded region to the right shows all the values of \( x \) that are greater than 2. The diagram helps to visualize the range of possible solutions for the inequality, making it easier to interpret.

**Significance:**
Number lines are essential for understanding inequalities, which are used in a wide range of mathematical and real-world applications, such as determining minimum or maximum values, solving optimization problems, and setting boundaries in various contexts.

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### Follow-Up Questions:
1. How does the slope of a line affect the graph of a linear equation?
2. What does the y-intercept represent in a linear equation?
3. How can you graph a linear inequality on a Cartesian plane?
4. What is the difference between strict inequalities (\( > \) or \( < \)) and inclusive inequalities (\( \geq \) or \( \leq \)) on a number line?
5. How would you solve a system of linear equations graphically?

### Tip:
When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number!

Create at least two visual representations (graphs, charts, diagrams) that illustrate key concepts from the unit. Provide a brief explanation for each visual, describing what it shows and its significance in the Solving Equations and Inequalities subject.

This page explains key concepts from the Solving Equations and Inequalities unit. It includes a graph of the linear equation y = 2x + 3 and a number line representing x ≥ 2, with explanations of their significance. Perfect for students in Grades 8-10.

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