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

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

For each point, the x-coordinate is \( 0 \). So, we substitute \( x = 0 \) into the inequality:

\[
y > 19(0) - 29
\]
\[
y > -29
\]

Now we will evaluate each of the given points:

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

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

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

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

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

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

The points that satisfy the inequality \( y > -29 \) are:

- \( \left(0, -\frac{4}{9}\right) \)
- (0, -19)
- \( \left(0, -\frac{1}{9}\right) \)
- (0, -13)

Among these, any of them can be considered a valid solution to the inequality \( y > 19x - 29 \).

If you are looking for one specific point as an answer, one of the options would be \( \left(0, -\frac{4}{9}\right) \).