Question

Which of the following points is a solution to the linear inequality y>1/9x−2/9 ?(1 point) Responses (0,−49) left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis (0,−29) left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis (0,−13) left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis (0,−19)

Answer 1

To determine which points are solutions to the linear inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we can substitute the x-coordinates of each point into the inequality and see if the resulting y-coordinate is greater than the expression on the right-hand side.

The inequality is:

\[
y > \frac{1}{9}x - \frac{2}{9}
\]

For x = 0, the inequality simplifies to:

\[
y > \frac{1}{9}(0) - \frac{2}{9} \implies y > -\frac{2}{9}
\]

Now we check each given point:

1. **Point (0, -49)**:
- y = -49
- Check: -49 > -2/9 (False)

2. **Point \( (0, -\frac{4}{9}) \)**:
- y = -\( \frac{4}{9} \)
- Check: -\( \frac{4}{9} \) > -\( \frac{2}{9} \) (False)

3. **Point (0, -29)**:
- y = -29
- Check: -29 > -2/9 (False)

4. **Point \( (0, -\frac{2}{9}) \)**:
- y = -\( \frac{2}{9} \)
- Check: -\( \frac{2}{9} \) > -\( \frac{2}{9} \) (False)

5. **Point (0, -13)**:
- y = -13
- Check: -13 > -2/9 (False)

6. **Point \( (0, -\frac{1}{3}) \)**:
- y = -\( \frac{1}{3} \) (which is -\( \frac{3}{9} \))
- Check: -\( \frac{3}{9} \) > -\( \frac{2}{9} \) (False)

7. **Point (0, -19)**:
- y = -19
- Check: -19 > -2/9 (False)

It appears that none of the given points satisfy the inequality \( y > -\frac{2}{9} \).

Please double-check the points or provide other options if the problem context allows prevailing confirmations.