Question

Which of the following points is a solution to the linear inequality y>19x−29
𝑦
>
1
9
𝑥
−
2
9
?(1 point)
Responses

(0,−13)
(
0
,
−
1
3
)
left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis

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

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

(0,−29)

Answer 1

To determine which point is a solution to the inequality \( y > 19x - 29 \), we can evaluate each option by substituting \( x = 0 \) into the inequality and checking if the resulting \( y \) value is greater than the right-hand side.

1. **Substituting \( x = 0 \)**:
\[
y > 19(0) - 29
\]
\[
y > -29
\]

Now we check each point:

1. **\( (0, -13) \)**:
\[
-13 > -29 \quad \text{(True)}
\]

2. **\( (0, -19) \)**:
\[
-19 > -29 \quad \text{(True)}
\]

3. **\( (0, -49) \)**:
\[
-49 > -29 \quad \text{(False)}
\]

4. **\( (0, -29) \)**:
\[
-29 > -29 \quad \text{(False)}
\]

The points \( (0, -13) \) and \( (0, -19) \) are solutions to the inequality. The point \( (0, -13) \) is a valid solution, as it is greater than \(-29\).

Thus, the correct responses among the choices provided include both \( (0, -13) \) and \( (0, -19) \). If you only need one response, \( (0, -13) \) is a satisfactory choice.