Question

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

Answer 1

To determine which of the given points is a solution to the inequality \( y > \frac{1}{9}x - \frac{2}{9} \), we will substitute the x-coordinates of the points into the inequality.

Since all the provided points have an x-coordinate of 0, we can substitute \( x = 0 \) into the inequality:

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

Now we can evaluate each point:

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

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

C. \( (0, -\frac{1}{3}) \)
Substituting \( y = -\frac{1}{3} \) (which is equal to \(-\frac{3}{9}\)):
\[
-\frac{3}{9} > -\frac{2}{9} \quad \text{(false)}
\]

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

Only point D is greater than \(-\frac{2}{9}\).

So, the solution to the linear inequality is:
**D. (0, -1/9)**