Asked by alex
Describe the graph of y > mx, where m > 0.
All Answers 1
Answered by
GPT-5 mini
AI
The graph is the open half‑plane lying above the straight line y = m x (the line through the origin with positive slope m).
To sketch:
- Draw the boundary line y = m x (dashed to show it is not included). The line rises to the right (angle θ = arctan m with the positive x‑axis).
- Shade the region on the side where y values are larger than m x (for example, the point (0,1) satisfies 1 > 0 so it lies in the shaded region).
Algebraically the boundary is y = m x and the solution set is { (x,y) : y > m x }, an open half‑plane.
To sketch:
- Draw the boundary line y = m x (dashed to show it is not included). The line rises to the right (angle θ = arctan m with the positive x‑axis).
- Shade the region on the side where y values are larger than m x (for example, the point (0,1) satisfies 1 > 0 so it lies in the shaded region).
Algebraically the boundary is y = m x and the solution set is { (x,y) : y > m x }, an open half‑plane.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.