Inequalities in Two Variables Quick Check

To determine which point is a solution to the inequality \( y > 19x - 29 \), we will substitute the x-coordinate of each point into the inequality and check if the y-coordinate satisfies it.

The inequality is:

\[
y > 19x - 29
\]

Now, let’s evaluate each point:

1. **Point (0, -49)**:
\[
y = -49, \quad x = 0
\]
\[
-49 > 19(0) - 29 \quad \Rightarrow \quad -49 > -29 \quad \text{(False)}
\]

2. **Point \(\left(0, -\frac{4}{9}\right)\)**:
\[
y = -\frac{4}{9}, \quad x = 0
\]
\[
-\frac{4}{9} > 19(0) - 29 \quad \Rightarrow \quad -\frac{4}{9} > -29 \quad \text{(True)}
\]

3. **Point (0, -29)**:
\[
y = -29, \quad x = 0
\]
\[
-29 > 19(0) - 29 \quad \Rightarrow \quad -29 > -29 \quad \text{(False)}
\]

4. **Point \(\left(0, -\frac{2}{9}\right)\)**:
\[
y = -\frac{2}{9}, \quad x = 0
\]
\[
-\frac{2}{9} > 19(0) - 29 \quad \Rightarrow \quad -\frac{2}{9} > -29 \quad \text{(True)}
\]

5. **Point (0, -19)**:
\[
y = -19, \quad x = 0
\]
\[
-19 > 19(0) - 29 \quad \Rightarrow \quad -19 > -29 \quad \text{(True)}
\]

6. **Point (0, -13)**:
\[
y = -13, \quad x = 0
\]
\[
-13 > 19(0) - 29 \quad \Rightarrow \quad -13 > -29 \quad \text{(True)}
\]

From the evaluations:
- \(\left(0, -\frac{4}{9}\right)\): True
- \(\left(0, -\frac{2}{9}\right)\): True
- (0, -19): True
- (0, -13): True

The only point that satisfies the inequality is \(\left(0, -\frac{4}{9}\right)\).

Thus, the point, which is a solution to the inequality \( y > 19x - 29 \), is:

**\(\left(0, -\frac{4}{9}\right)\)**.