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,−29) left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis (0,−19) left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis (0,−13) left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis

1 answer

To determine which of the given points is a solution to the inequality \( y > 19x - 29 \), we can substitute \( x = 0 \) for each point and check if the corresponding \( y \) value satisfies the inequality.

The equation \( y = 19x - 29 \) simplifies to:

  • For \( x = 0 \): \[ y = 19(0) - 29 = -29 \]

Now, we can compare the y-values of the given points with \(-29\):

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

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

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

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

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

  6. Point (0, -1/9): \[ -\frac{1}{9} > -29 \quad \text{(True)} \]

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

Thus, points (0, -4/9), (0, -2/9), (0, -19), (0, -1/9), and (0, -13) are all solutions to the inequality \( y > 19x - 29 \).

However, since we were just to choose a single point as a solution, (0, -4/9) is a correct answer.

So, the answer is (0, -4/9).