Question

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Which of the following points is a part of the solution set for the inequality y≥3x-1

(1, 1)
(-1, -5)
(2, 5)
(-2.5, -9)

Answer 1

To determine which of the given points is a part of the solution set for the inequality \( y \geq 3x - 1 \), we will substitute each point into the inequality and check if it holds true.

1. **Point (1, 1):**
- Substitute \( x = 1 \) and \( y = 1 \):
\[
1 \geq 3(1) - 1
\]
\[
1 \geq 3 - 1
\]
\[
1 \geq 2 \quad \text{(False)}
\]

2. **Point (-1, -5):**
- Substitute \( x = -1 \) and \( y = -5 \):
\[
-5 \geq 3(-1) - 1
\]
\[
-5 \geq -3 - 1
\]
\[
-5 \geq -4 \quad \text{(False)}
\]

3. **Point (2, 5):**
- Substitute \( x = 2 \) and \( y = 5 \):
\[
5 \geq 3(2) - 1
\]
\[
5 \geq 6 - 1
\]
\[
5 \geq 5 \quad \text{(True)}
\]

4. **Point (-2.5, -9):**
- Substitute \( x = -2.5 \) and \( y = -9 \):
\[
-9 \geq 3(-2.5) - 1
\]
\[
-9 \geq -7.5 - 1
\]
\[
-9 \geq -8.5 \quad \text{(False)}
\]

After evaluating all the points, we find that:

- (1, 1) is false.
- (-1, -5) is false.
- (2, 5) is true.
- (-2.5, -9) is false.

**Therefore, the only point that is part of the solution set for the inequality \( y \geq 3x - 1 \) is (2, 5).**

Answer 2

Please make it way shorter

Answer 3

To check which points satisfy \( y \geq 3x - 1 \):

1. **Point (1, 1)**:
\[
1 \geq 3(1) - 1 \implies 1 \geq 2 \quad \text{(False)}
\]

2. **Point (-1, -5)**:
\[
-5 \geq 3(-1) - 1 \implies -5 \geq -4 \quad \text{(False)}
\]

3. **Point (2, 5)**:
\[
5 \geq 3(2) - 1 \implies 5 \geq 5 \quad \text{(True)}
\]

4. **Point (-2.5, -9)**:
\[
-9 \geq 3(-2.5) - 1 \implies -9 \geq -8.5 \quad \text{(False)}
\]

**Conclusion**: The point **(2, 5)** is the only one that satisfies the inequality.

Answer 4

Just a little Shorter please

Answer 5

To check which points satisfy \( y \geq 3x - 1 \):

1. **(1, 1)**: \( 1 \geq 2 \) (False)
2. **(-1, -5)**: \( -5 \geq -4 \) (False)
3. **(2, 5)**: \( 5 \geq 5 \) (True)
4. **(-2.5, -9)**: \( -9 \geq -8.5 \) (False)

**Conclusion**: The point **(2, 5)** is the only solution.