Question

Which of the following points is a solution to the linear inequality y>19x−29 ?(1 point)
Responses

(0,−29)
left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis

(0,−49)
left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis

(0,−19)
left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis

(0,−13)

Answer 1

To determine which of the given points is a solution to the linear inequality \( y > 19x - 29 \), we will substitute the x-coordinates of each point into the inequality and see if the resulting y-value satisfies the inequality.

The inequality is:
\[ y > 19x - 29 \]

Now, we will evaluate each point:

1. **Point (0, -29)**:
- Substitute \( x = 0 \):
\[
y > 19(0) - 29 \implies y > -29
\]
- Check: \( -29 > -29 \) (false). This point does **not** satisfy the inequality.

2. **Point \( (0, -\frac{2}{9}) \)**:
- Substitute \( x = 0 \):
\[
y > 19(0) - 29 \implies y > -29
\]
- Check: \( -\frac{2}{9} > -29 \) (true). This point satisfies the inequality.

3. **Point (0, -49)**:
- Substitute \( x = 0 \):
\[
y > 19(0) - 29 \implies y > -29
\]
- Check: \( -49 > -29 \) (false). This point does **not** satisfy the inequality.

4. **Point \( (0, -\frac{4}{9}) \)**:
- Substitute \( x = 0 \):
\[
y > 19(0) - 29 \implies y > -29
\]
- Check: \( -\frac{4}{9} > -29 \) (true). This point also satisfies the inequality.

5. **Point (0, -19)**:
- Substitute \( x = 0 \):
\[
y > 19(0) - 29 \implies y > -29
\]
- Check: \( -19 > -29 \) (true). This point satisfies the inequality.

6. **Point (0, -13)**:
- Substitute \( x = 0 \):
\[
y > 19(0) - 29 \implies y > -29
\]
- Check: \( -13 > -29 \) (true). This point satisfies the inequality.

From the evaluations above, the following points satisfy the inequality \( y > 19x - 29 \):
- \( (0, -\frac{2}{9}) \)
- \( (0, -\frac{4}{9}) \)
- \( (0, -19) \)
- \( (0, -13) \)

However, since the question requests a single point, we can conclude that:
- The point \( (0, -\frac{2}{9}) \) is one valid solution.

So, the answer is \( (0, -\frac{2}{9}) \).