Question

Which of the following points is a solution to the linear inequality y>1/9x−2/9?(1 point)
A: (0,−2/9)
B:(0,−4/9)
C: (0,−1/3)
D; 0,−1/9)

Answer 1

To determine which of the points is a solution 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 corresponding y-coordinates satisfy it.

The inequality can be expressed for \( x = 0 \):

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

Now we can check each point:

A: \( (0, -\frac{2}{9}) \)
- Substitute \( y = -\frac{2}{9} \):
\[
-\frac{2}{9} > -\frac{2}{9} \quad \text{(false)}
\]

B: \( (0, -\frac{4}{9}) \)
- Substitute \( y = -\frac{4}{9} \):
\[
-\frac{4}{9} > -\frac{2}{9} \quad \text{(false)}
\]

C: \( (0, -\frac{1}{3}) \)
- Substitute \( y = -\frac{1}{3} \approx -\frac{3}{9} \):
\[
-\frac{1}{3} > -\frac{2}{9} \quad \text{(false)}
\]

D: \( (0, -\frac{1}{9}) \)
- Substitute \( y = -\frac{1}{9} \):
\[
-\frac{1}{9} > -\frac{2}{9} \quad \text{(true)}
\]

The only point that satisfies the inequality is:

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