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,−29) left parenthesis 0 comma negative Start Fraction 2 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 evaluate each point by plugging the \(x\) and \(y\) values into the inequality.

The inequality can be expressed as:

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

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

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

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

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

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

Now, let's summarize which points satisfy the inequality \( y > 19x - 29 \):

- Points that are solutions: \( (0, -13) \), \( \left(0, -\frac{1}{3}\right) \), \( \left(0, -\frac{4}{9}\right) \), \( (0, -19) \).
- Points that are not solutions: \( (0, -49) \), \( (0, -29) \).

Thus, the correct responses are:

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

You can choose any of the points that are solutions.