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

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

(0,−13)

Answer 1

answer

Answer 2

To determine which of the given points is a solution to the linear inequality \( y > 19x - 29 \), we can substitute the x-coordinates of each point (which are all 0) into the inequality and see if the corresponding y-coordinates satisfy it.

The inequality simplifies to:
\[ y > 19(0) - 29 \]
\[ y > -29 \]

Now, we will check each point to see if its y-coordinate is greater than -29.

1. **Point (0, -49)**:
\[ -49 > -29 \] → False

2. **Point \( \left(0, -\frac{4}{9}\right) \)**:
\[ -\frac{4}{9} > -29 \] → True (since -4/9 is greater than -29)

3. **Point (0, -19)**:
\[ -19 > -29 \] → True

4. **Point \( \left(0, -\frac{1}{9}\right) \)**:
\[ -\frac{1}{9} > -29 \] → True

5. **Point (0, -29)**:
\[ -29 > -29 \] → False

6. **Point \( \left(0, -\frac{2}{9}\right) \)**:
\[ -\frac{2}{9} > -29 \] → True

7. **Point (0, -13)**:
\[ -13 > -29 \] → True

From the checks above, the following points satisfy the inequality \( y > -29 \):
- \( \left(0, -\frac{4}{9}\right) \)
- (0, -19)
- \( \left(0, -\frac{1}{9}\right) \)
- \( \left(0, -\frac{2}{9}\right) \)
- (0, -13)

Thus, the points (0, -19), \( \left(0, -\frac{4}{9}\right) \), \( \left(0, -\frac{1}{9}\right) \), \( \left(0, -\frac{2}{9}\right) \), and (0, -13) are solutions to the inequality.

Depending on the specific wording of the question, the response could refer to any of these valid points. If you need one specific point, I suggest \( (0, -19) \) as it is one of the responses listed in the original options.