Draw the graphs of the inequality `ylex`.

Answer

To solve the inequality \( y \leq x \) and draw its graph, we will follow these steps:

### Step 1: Understand the inequality
The inequality \( y \leq x \) means that for any point (x, y) on the graph, the value of y should be less than or equal to the value of x.

### Step 2: Convert the inequality to an equation
To start, we will first consider the equality \( y = x \). This will help us understand the boundary line for our inequality.

### Step 3: Draw the graph of the equation
1. **Plot the line \( y = x \)**:
- The line \( y = x \) is a straight line that passes through the origin (0,0) and has a slope of 1.
- You can plot points such as (1,1), (2,2), (-1,-1), etc., and draw a straight line through these points.

### Step 4: Determine the type of line
Since the inequality is \( y \leq x \), we will use a solid line for \( y = x \) because the inequality includes equal to (≤).

### Step 5: Identify the shaded region
1. **Shading the appropriate region**:
- The inequality \( y \leq x \) indicates that we need to shade the region below the line \( y = x \) (including the line itself).
- This means for any point in this shaded area, the y-coordinate will be less than or equal to the x-coordinate.

### Step 6: Finalize the graph
1. **Complete the graph**:
- Ensure that the line is solid, and the area below it is shaded to represent all the points (x, y) where \( y \leq x \).

### Summary of the Graph
- The graph consists of a solid line along \( y = x \) and the shaded area below this line.

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