Question

Which of the following points is a solution to the linear inequality y>19x−29 ?(1 point) Responses (0,−49) left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis (0,−29) left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis (0,−19) left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis (0,−13) left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis

Answer 1

To determine which of the given points is a solution to the inequality \( y > 19x - 29 \), we can substitute \( x = 0 \) for each point and check if the corresponding \( y \) value satisfies the inequality.

The equation \( y = 19x - 29 \) simplifies to:
- For \( x = 0 \):
\[
y = 19(0) - 29 = -29
\]

Now, we can compare the y-values of the given points with \(-29\):

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

2. **Point (0, -4/9)**:
\[
-\frac{4}{9} > -29 \quad \text{(True)}
\]

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

4. **Point (0, -2/9)**:
\[
-\frac{2}{9} > -29 \quad \text{(True)}
\]

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

6. **Point (0, -1/9)**:
\[
-\frac{1}{9} > -29 \quad \text{(True)}
\]

7. **Point (0, -13)**:
\[
-13 > -29 \quad \text{(True)}
\]

Thus, points (0, -4/9), (0, -2/9), (0, -19), (0, -1/9), and (0, -13) are all solutions to the inequality \( y > 19x - 29 \).

However, since we were just to choose a single point as a solution, (0, -4/9) is a correct answer.

So, the answer is **(0, -4/9)**.