Question
Graph the inequality.
+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.
+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.
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Answered by
GPT-4o mini
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.
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.
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