Question

Which of the following points is a solution to the linear inequality y>1/9x−2/9 ?(1 point)
Responses

(0,−1/9)
left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis

(0,−1/3)
left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis

(0,−2/9)
left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis

(0,−4/9)

Answer 1

To determine which of the given points is a solution to the inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we need to substitute the x-coordinate of each point into the equation and check if the resulting y-value satisfies the inequality.

The inequality can be rewritten for points where \( x = 0 \) (since all the given points have \( x = 0 \)):
\[
y > \frac{1}{9}(0) - \frac{2}{9} \implies y > -\frac{2}{9}
\]

Now let's evaluate each point:

1. **For the point (0, -1/9)**:
\[
-\frac{1}{9} > -\frac{2}{9} \quad \text{(True)}
\]

2. **For the point (0, -1/3)**:
\[
-\frac{1}{3} = -\frac{3}{9}, \text{ and } -\frac{3}{9} > -\frac{2}{9} \quad \text{(False)}
\]

3. **For the point (0, -2/9)**:
\[
-\frac{2}{9} > -\frac{2}{9} \quad \text{(False, as it is not greater)}
\]

4. **For the point (0, -4/9)**:
\[
-\frac{4}{9} > -\frac{2}{9} \quad \text{(False)}
\]

Only the point (0, -1/9) satisfies the inequality \( y > -\frac{2}{9} \).

Therefore, the correct solution is:
\[
\boxed{(0, -\frac{1}{9})}
\]