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,−29) left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis (0,−49) left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis (0,−19)

Answer 1

To determine which of the given points is a solution to the linear inequality \( y > 19x - 29 \), we can plug in the x-coordinates of the points into the inequality and see if the corresponding y-coordinates satisfy it.

1. Point (0, -13): \[ y > 19(0) - 29 \implies -13 > -29 \quad \text{(True)} \]

2. Point (0, -\frac{1}{3}): \[ y > 19(0) - 29 \implies -\frac{1}{3} > -29 \quad \text{(True)} \]

3. Point (0, -29): \[ y > 19(0) - 29 \implies -29 > -29 \quad \text{(False)} \]

4. Point (0, -\frac{2}{9}): \[ y > 19(0) - 29 \implies -\frac{2}{9} > -29 \quad \text{(True)} \]

5. Point (0, -49): \[ y > 19(0) - 29 \implies -49 > -29 \quad \text{(False)} \]

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

From the evaluation above, the solutions to the inequality \( y > 19x - 29 \) are the points (0, -13), (0, -\frac{1}{3}), (0, -\frac{2}{9}), and (0, -19). The points (0, -29) and (0, -49) do not satisfy the inequality.

Thus, any of the points (0, -13), (0, -\frac{1}{3}), (0, -\frac{2}{9}), or (0, -19) are valid solutions.