Question

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

(0, -4/9)
(0, -1/3)
(0, -1/9)
(0, -2/9)

Answer 1

To determine which points are solutions to the inequality \(y > \frac{1}{9}x - \frac{2}{9}\), we can evaluate the right side of the inequality for each point where \(x = 0\).

1. For the point \((0, -\frac{4}{9})\):
\[
y = -\frac{4}{9}, \quad \text{and } y > \frac{1}{9}(0) - \frac{2}{9} = -\frac{2}{9}
\]
\(-\frac{4}{9} > -\frac{2}{9}\) is **false**.

2. For the point \((0, -\frac{1}{3})\):
\[
y = -\frac{1}{3}, \quad \text{and } y > \frac{1}{9}(0) - \frac{2}{9} = -\frac{2}{9}
\]
\(-\frac{1}{3} > -\frac{2}{9}\) is **false** (since \(-\frac{1}{3} \equiv -\frac{3}{9}\), \(-\frac{3}{9} > -\frac{2}{9}\) is not true).

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

4. For the point \((0, -\frac{2}{9})\):
\[
y = -\frac{2}{9}, \quad \text{and } y > \frac{1}{9}(0) - \frac{2}{9} = -\frac{2}{9}
\]
\(-\frac{2}{9} > -\frac{2}{9}\) is **false**.

The only point that satisfies the inequality is:

\((0, -\frac{1}{9})\).