Question

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

(0,−13)
left parenthesis 0 comma negative Start Fraction 1 over 3 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,−29)

Answer 1

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 into the inequality and check if the y-coordinates satisfy the inequality.

1. For point \( (0, -13) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -13 > -29 \) (True).

2. For point \( (0, -\frac{1}{3}) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -\frac{1}{3} > -29 \) (True).

3. For point \( (0, -49) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -49 > -29 \) (False).

4. For point \( (0, -\frac{4}{9}) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -\frac{4}{9} > -29 \) (True).

5. For point \( (0, -19) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -19 > -29 \) (True).

6. For point \( (0, -29) \):
- Substitute \( x = 0 \): \( y > 19(0) - 29 \) becomes \( y > -29 \).
- Check \( -29 > -29 \) (False, since it needs to be greater than).

From the calculations, the points that satisfy the inequality \( y > 19x - 29 \) are:
- \( (0, -13) \)
- \( (0, -\frac{1}{3}) \)
- \( (0, -\frac{4}{9}) \)
- \( (0, -19) \)

Thus, any of the first four points are valid solutions, but the point \( (0, -29) \) is not.