Question

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

(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

(0,−49)

Answer 1

To determine which point is a solution to the linear inequality \( y > 19x - 29 \), we will evaluate each point by substituting the \( x \) and \( y \) coordinates into the inequality.

The inequality is:
\[ y > 19x - 29 \]

1. **For the point (0, -29)**:
\[
y = -29, \quad x = 0
\]
\[
-29 > 19(0) - 29
\]
\[
-29 > -29 \quad \text{(false)}
\]

2. **For the point (0, -2/9)**:
\[
y = -\frac{2}{9}, \quad x = 0
\]
\[
-\frac{2}{9} > 19(0) - 29
\]
\[
-\frac{2}{9} > -29 \quad \text{(true)}
\]

3. **For the point (0, -19)**:
\[
y = -19, \quad x = 0
\]
\[
-19 > 19(0) - 29
\]
\[
-19 > -29 \quad \text{(true)}
\]

4. **For the point (0, -13)**:
\[
y = -13, \quad x = 0
\]
\[
-13 > 19(0) - 29
\]
\[
-13 > -29 \quad \text{(true)}
\]

5. **For the point (0, -49)**:
\[
y = -49, \quad x = 0
\]
\[
-49 > 19(0) - 29
\]
\[
-49 > -29 \quad \text{(false)}
\]

Thus, the points that are solutions to the inequality \( y > 19x - 29 \) are:

- \( (0, -\frac{2}{9}) \)
- \( (0, -19) \)
- \( (0, -13) \)

Therefore, any of the points \( (0, -\frac{2}{9}) \), \( (0, -19) \), or \( (0, -13) \) can be considered a solution to the inequality.