Shade the region given by inequality
` x + y lt 5`

Explanation

To solve the inequality \( x + y < 5 \) and shade the appropriate region, follow these steps:

### Step 1: Rewrite the inequality
The inequality given is \( x + y < 5 \). We can rewrite it as an equation to find the boundary line:
\[ x + y = 5 \]

### Step 2: Find intercepts
To graph the line \( x + y = 5 \), we can find the x-intercept and y-intercept.

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

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

### Step 3: Plot the intercepts
On a coordinate plane, plot the points \( (5, 0) \) and \( (0, 5) \).

### Step 4: Draw the boundary line
Draw a dashed line through the points \( (5, 0) \) and \( (0, 5) \). The dashed line indicates that the points on the line are not included in the solution (since the inequality is strict, \( < \)).

### Step 5: Determine the shaded region
To find which side of the line to shade, we can test a point not on the line. A convenient point to test is the origin \( (0, 0) \).

Substituting \( (0, 0) \) into the inequality:
\[ 0 + 0 < 5 \implies 0 < 5 \quad \text{(True)} \]
Since this is true, we shade the region that includes the origin.

### Step 6: Finalize the graph
Shade the region below the line \( x + y = 5 \) (the region that includes the origin).

### Summary
The shaded region represents all the points \( (x, y) \) that satisfy the inequality \( x + y < 5 \).

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