Graph the inequality.

To graph the inequality \( y < x + 5 \), follow these steps:

1. Graph the Boundary Line:

   • The boundary line is given by the equation \( y = x + 5 \). This is a straight line with a slope of 1 and a y-intercept of 5.
   • To graph this line, plot the y-intercept at (0, 5).
   • From that point, use the slope to find another point. Since the slope is 1, you can go up 1 unit and right 1 unit to find the point (1, 6), or down 1 unit and left 1 unit to find (−1, 4).
   • Connect these points with a dashed line because the inequality is strict (<), indicating that points on the line are not included in the solution set.

2. Shade the Appropriate Region:

   • Since the inequality is \( y < x + 5 \), you will shade the area below the line. This means for any point in this shaded region, the y-value is less than the corresponding y-value of the line.

Here’s a summary of the graphing steps:

• Draw a dashed line for \( y = x + 5 \).
• Shade the region below this line.

Graph Representation

If you were to visualize this graph:

• The x-axis runs horizontally, and the y-axis runs vertically.
• Mark the line \( y = x + 5 \) with a dashed line.
• Shade everything below this line.

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