Describe the graph of y > mx, where m > 0.
Straight lines can be used to represent linear equations in the cartesian plane. Using these linear equations, we can extract various information about the equations.
Answer: The graph of y > mx, where m > 0, contains the entire 2nd quadrant and the 1st and the 3rd quadrant partially.
Let's understand the solution in detail.
Given equation: y > mx, m > 0.
Now, since m > 0, therefore, the line corresponding to the inequality will always have a positive slope.
Now, let's substitute some values of m in the inequality above:
⇒ If m = 1, then y > x.
⇒ If m = 2, then y > 2x.
Now, if we substitute the point (-1, 1) in y > 2x, then we see that the inequality is true. Hence, the area covered by the inequality contains (-1, 1).
Now, let's represent this on the graph.
The shaded region covers the second quadrant and parts of the first and third quadrants.