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

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

(0,−29)

Answer 1

To determine which of the given points is a solution to the inequality \( y > 19x - 29 \), we can substitute the \( x \) and \( y \) values from each point into the inequality and check if it holds true.

The inequality in terms of \( x \) and \( y \) is:

\[
y > 19x - 29
\]

Let's evaluate each option by substituting \( x = 0 \) into the inequality.

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

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

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

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

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

Based on the evaluations, all points except (0, -29) satisfy the inequality \( y > 19x - 29 \). Therefore, the solutions to the inequality are:

- (0, -13)
- \( \left(0, -\frac{1}{3}\right) \)
- (0, -19)
- \( \left(0, -\frac{4}{9}\right) \)

Hence, any of the first four points can be considered a solution, but the first four options listed are valid responses.