Graph the following linear inequality y> x -2. Show or explain on the graph the region where the solution to the inequality would be.
To graph the linear inequality y > x - 2, we can first graph the line y = x - 2, and then shade the region above the line.
To graph the line y = x - 2, we can start by plotting two points. Let's choose the points (0, -2) and (2, 0).
When x = 0, y = 0 - 2 = -2. So the first point is (0, -2).
When x = 2, y = 2 - 2 = 0. So the second point is (2, 0).
Plotting these points on a graph and drawing a line through them, we get:
|
|
|
|
(2,0)|
-------------------
| .
| .
| .
| .
(0,-2)|
----------------------
Next, we need to shade the region above the line y = x - 2. Since the inequality is y > x - 2, the "greater than" symbol indicates that we need to shade the region above the line.
Shading the region above the line, we get:
|▓▓▓▓▓▓▓▓▓▓▓
|▓▓▓▓▓▓▓▓▓▓▓
|▓▓▓▓▓▓▓▓▓▓▓
|▓▓▓▓▓▓▓▓▓▓▓
(2,0)|▓▓▓▓▓▓▓▓▓▓▓
-------------------
| ▓.
| ▓.
| ▓.
| ▓.
(0,-2)| ▓▓.
----------------------
The shaded region above the line y = x - 2 represents the solution to the inequality y > x - 2.