Which of the following points is a solution to the linear inequality y > 1/9x - 2/9?

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
24 days ago

To determine if a point is a solution to the linear inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we will need to test various points by substituting their coordinates into the inequality.

Let's describe the steps you'd follow:

1. **Choose a point**: Pick a point (x, y).
2. **Substitute**: Replace x and y in the inequality with the chosen point’s coordinates.
3. **Evaluate the inequality**: Check if the result satisfies the inequality \( y > \frac{1}{9}x - \frac{2}{9} \).

Let's test a few points:

1. **Point (0, 0)**:
- Substitute into the inequality:
\( 0 > \frac{1}{9}(0) - \frac{2}{9} \) → \( 0 > -\frac{2}{9} \) (True)

2. **Point (9, 1)**:
- Substitute into the inequality:
\( 1 > \frac{1}{9}(9) - \frac{2}{9} \) → \( 1 > 1 - \frac{2}{9} \) → \( 1 > \frac{7}{9} \) (True)

3. **Point (9, 0)**:
- Substitute into the inequality:
\( 0 > \frac{1}{9}(9) - \frac{2}{9} \) → \( 0 > 1 - \frac{2}{9} \) → \( 0 > \frac{7}{9} \) (False)

4. **Point (0, -1)**:
- Substitute into the inequality:
\( -1 > \frac{1}{9}(0) - \frac{2}{9} \) → \( -1 > -\frac{2}{9} \) (False)

Choose points to test until you find one that satisfies the inequality.

If you have specific points you'd like to test, please share them, and I can help evaluate them!