Solve the inequation `x + y lt 5` by graphical method.

Explanation

To solve the inequality \( x + y < 5 \) using the graphical method, we will follow these steps:

### Step 1: Rewrite the Inequality
We start with the given inequality:
\[ x + y < 5 \]
To analyze this graphically, we can first rewrite it as an equation:
\[ x + y = 5 \]

### Step 2: Find Intercepts
Next, we will find the intercepts of the line \( x + y = 5 \).

- **Finding the y-intercept**: Set \( x = 0 \).
\[ 0 + y = 5 \implies y = 5 \]
So, the y-intercept is \( (0, 5) \).

- **Finding the x-intercept**: Set \( y = 0 \).
\[ x + 0 = 5 \implies x = 5 \]
So, the x-intercept is \( (5, 0) \).

### Step 3: Plot the Line
Now, we will plot the line \( x + y = 5 \) on a graph. We have two points:
- \( (0, 5) \)
- \( (5, 0) \)

Draw a straight line through these two points. Since the inequality is strict (\(<\)), we will use a dashed line to indicate that points on the line itself are not included in the solution.

### Step 4: Determine the Shaded Region
To find which side of the line to shade, we can test a point that is not on the line. A convenient point to test is the origin \( (0, 0) \).

Substituting \( (0, 0) \) into the inequality:
\[ 0 + 0 < 5 \implies 0 < 5 \]
This statement is true, so we shade the region that includes the origin.

### Step 5: Final Graph
The graph will show the dashed line representing \( x + y = 5 \) and the shaded region below this line, indicating all points \( (x, y) \) that satisfy the inequality \( x + y < 5 \).

### Conclusion
The solution to the inequality \( x + y < 5 \) is represented by the shaded region below the line \( x + y = 5 \) on the graph.

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