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,−2/9)
left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis
(0,−1/3)
left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis
(0,−4/9)

Answer 1

To determine which of the provided points is a solution to the inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we can substitute each point into the inequality and see if it holds true.

The inequality can be rewritten for easy computation with \( x = 0 \):

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

Now, we can evaluate each of the points:

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

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

3. **Point (0, -1/3)**:
\[
-\frac{1}{3} > -\frac{2}{9} \quad \text{(False, since -1/3 = -3/9 which is less than -2/9)}
\]

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

Based on the evaluations, the only point that satisfies the inequality \( y > -\frac{2}{9} \) is **(0, -1/9)**.

Thus, the solution to the inequality is:

**(0, -1/9)**.