Graph the inequality.

Question

+5
y<x+5

Select an option for your boundary line:

Turn on the shading option and move the black point to show where to shade the half-plane.

Answer 1

To graph the inequality \( y < x + 5 \):

1. Identify the boundary line: The equation \( y = x + 5 \) represents a line that will be our boundary. Since the inequality is strict (using "<"), the line should be dashed to indicate that points on the line are not included in the solution.

2. Graph the line:

   • Start at the y-intercept (0, 5).
   • Use the slope (1) to find another point. From (0, 5), go up 1 unit and right 1 unit to (1, 6).
   • Draw a dashed line through these points.

3. Shade the appropriate half-plane: Since the inequality is \( y < x + 5 \), you will shade below the line:

   • Choose a test point not on the line, such as (0, 0).
   • Substitute this point into the inequality: \( 0 < 0 + 5 \) which is true. Therefore, shade the region that contains (0, 0), which is below the line.

Now your graph should show a dashed line for \( y = x + 5 \) with the half-plane below the line shaded.

If you have graphical tools that allow you to turn on shading or move points, be sure to reflect these steps in that interface.