Which of the following points is a solution to the linear inequality y>19x−29

Question

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.