Question
Which is the graph of the linear inequality y < 3x + 1?On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
2. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Everything to the right of the line is shaded.Which linear inequality is represented by the graph?y ≥ One-thirdx – 4y ≤ One-thirdx – 4y ≤ One-thirdx + 4y ≥ One-thirdx + 4
3. Which statements are true about the linear inequality y > Three-fourthsx – 2? Select three options.
The slope of the line is –2.
The graph of y > Three-fourthsx – 2 is a dashed line.
The area below the line is shaded.
One solution to the inequality is (0, 0).
The graph intercepts the y-axis at (0, –2).
4. Which is the graph of the linear inequality 2x – 3y < 12?On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
5. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.Which linear inequality is represented by the graph?y < 3x + 2y > 3x + 2y < One-thirdx + 2y > One-thirdx + 2
6. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded.Which linear inequality is represented by the graph?y ≤ One-halfx + 2y ≥ One-halfx + 2y ≤ One-thirdx + 2y ≥ One-thirdx + 2
7. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything below the line is shaded.Which points are solutions to the linear inequality y < 0.5x + 2? Select three options.(–3, –2) (–2, 1)(–1, –2)(–1, 2)(1, –2)
8. Which is the graph of linear inequality 2y > x – 2?On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the right of the line is shaded.On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the right of the line is shaded.
9. On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.Which linear inequality is represented by the graph?y ≤ One-thirdx − 1y ≥ One-thirdx − 1y < 3x − 1y > 3x − 1
10. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 1) and (1, 0). Everything to the left of the line is shaded.The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?(2, 3)(3, –2)(2, 1)(–1, 3)
2. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Everything to the right of the line is shaded.Which linear inequality is represented by the graph?y ≥ One-thirdx – 4y ≤ One-thirdx – 4y ≤ One-thirdx + 4y ≥ One-thirdx + 4
3. Which statements are true about the linear inequality y > Three-fourthsx – 2? Select three options.
The slope of the line is –2.
The graph of y > Three-fourthsx – 2 is a dashed line.
The area below the line is shaded.
One solution to the inequality is (0, 0).
The graph intercepts the y-axis at (0, –2).
4. Which is the graph of the linear inequality 2x – 3y < 12?On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
5. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.Which linear inequality is represented by the graph?y < 3x + 2y > 3x + 2y < One-thirdx + 2y > One-thirdx + 2
6. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded.Which linear inequality is represented by the graph?y ≤ One-halfx + 2y ≥ One-halfx + 2y ≤ One-thirdx + 2y ≥ One-thirdx + 2
7. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything below the line is shaded.Which points are solutions to the linear inequality y < 0.5x + 2? Select three options.(–3, –2) (–2, 1)(–1, –2)(–1, 2)(1, –2)
8. Which is the graph of linear inequality 2y > x – 2?On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the right of the line is shaded.On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the right of the line is shaded.
9. On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 1) and (3, 0). Everything above and to the left of the line is shaded.Which linear inequality is represented by the graph?y ≤ One-thirdx − 1y ≥ One-thirdx − 1y < 3x − 1y > 3x − 1
10. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 1) and (1, 0). Everything to the left of the line is shaded.The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?(2, 3)(3, –2)(2, 1)(–1, 3)
Answers
Answered by
GPT-4o mini
Let's break down each question step by step.
### 1. Which is the graph of the linear inequality \( y < 3x + 1 \)?
- Since the inequality is "less than" (<), the line will be **dashed**.
- The line \( y = 3x + 1 \) has a positive slope. The shaded region would be **below the line**.
- Thus, the correct choice is:
**On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything below the line is shaded.**
### 2. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Which linear inequality is represented by the graph?
- The line is solid, indicating the inequality is **greater than or equal to (≥)**.
- The slope can be calculated; focusing on the points provided, the line equation might be a form like \( y \ge \frac{1}{3}x - 4 \).
- Thus, the correct choice is:
**y ≥ One-thirdx – 4.**
### 3. Which statements are true about the linear inequality \( y > \frac{3}{4}x - 2 \)? (Select three options.)
- True statements are:
- The graph of \( y > \frac{3}{4}x - 2 \) is a **dashed line**.
- **One solution to the inequality is (0, 0),** since substituting \( x = 0 \) gives \( y > -2 \).
- The graph intercepts the y-axis at **(0, -2)**.
- The slope is not -2; it is \( \frac{3}{4} \).
- Thus, the true statements are:
- The graph of \( y > \frac{3}{4}x - 2 \) is a dashed line.
- One solution to the inequality is (0, 0).
- The graph intercepts the y-axis at (0, -2).
### 4. Which is the graph of the linear inequality \( 2x - 3y < 12 \)?
- The line \( 2x - 3y = 12 \) can be rearranged into slope-intercept form.
- The line is dashed because the inequality is "less than."
- The shaded region will be **below the line**.
- Thus, the correct choice is:
**On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.**
### 5. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Which linear inequality is represented by the graph?
- The line is dashed, indicating a strict inequality.
- The shaded region is below the line, giving the inequality:
**y < 3x + 2** (derived from the slope).
### 6. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Which linear inequality is represented by the graph?
- Since the line is solid, it represents an "equal to" situation as well.
- Everything to the right is shaded, indicating:
**y ≥ One-halfx + 2.**
### 7. Which points are solutions to the linear inequality \( y < 0.5x + 2 \)? (Select three options.)
- Evaluate each point:
- (–3, –2): LHS = -2, RHS = 0.5*(-3)+2 = 0.5. Yes.
- (–2, 1): LHS = 1, RHS = 0.5*(-2)+2 = 1. No.
- (–1, –2): LHS = -2, RHS = 0.5*(-1)+2 = 1. Yes.
- (–1, 2): LHS = 2, RHS = 0.5*(-1)+2 = 1. No.
- (1, –2): LHS = -2, RHS = 0.5*(1)+2 = 2. No.
- Thus, the solutions are:
**(–3, –2), (–1, –2)**.
### 8. Which is the graph of the linear inequality \( 2y > x - 2 \)?
- The line is dashed indicating strict inequality.
- Everything above the line represents:
**On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything above the line is shaded.**
### 9. Which linear inequality is represented by the graph?
- Solid line indicates ≤ or ≥, everything above indicates:
**y ≥ One-thirdx - 1.**
### 10. Which point is a solution to the inequality \( y ≤ -x + 1 \)?
- Evaluate the points:
- (2, 3): LHS = 3, RHS = -2. No.
- (3, –2): LHS = -2, RHS = -2. Yes (on the boundary).
- (2, 1): LHS = 1, RHS = -1. No.
- (–1, 3): LHS = 3, RHS = 2. No.
- Thus, the solution is:
**(3, –2).**
Feel free to ask if you have any further questions!
### 1. Which is the graph of the linear inequality \( y < 3x + 1 \)?
- Since the inequality is "less than" (<), the line will be **dashed**.
- The line \( y = 3x + 1 \) has a positive slope. The shaded region would be **below the line**.
- Thus, the correct choice is:
**On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything below the line is shaded.**
### 2. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 3, negative 5) and (0, negative 4). Which linear inequality is represented by the graph?
- The line is solid, indicating the inequality is **greater than or equal to (≥)**.
- The slope can be calculated; focusing on the points provided, the line equation might be a form like \( y \ge \frac{1}{3}x - 4 \).
- Thus, the correct choice is:
**y ≥ One-thirdx – 4.**
### 3. Which statements are true about the linear inequality \( y > \frac{3}{4}x - 2 \)? (Select three options.)
- True statements are:
- The graph of \( y > \frac{3}{4}x - 2 \) is a **dashed line**.
- **One solution to the inequality is (0, 0),** since substituting \( x = 0 \) gives \( y > -2 \).
- The graph intercepts the y-axis at **(0, -2)**.
- The slope is not -2; it is \( \frac{3}{4} \).
- Thus, the true statements are:
- The graph of \( y > \frac{3}{4}x - 2 \) is a dashed line.
- One solution to the inequality is (0, 0).
- The graph intercepts the y-axis at (0, -2).
### 4. Which is the graph of the linear inequality \( 2x - 3y < 12 \)?
- The line \( 2x - 3y = 12 \) can be rearranged into slope-intercept form.
- The line is dashed because the inequality is "less than."
- The shaded region will be **below the line**.
- Thus, the correct choice is:
**On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.**
### 5. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Which linear inequality is represented by the graph?
- The line is dashed, indicating a strict inequality.
- The shaded region is below the line, giving the inequality:
**y < 3x + 2** (derived from the slope).
### 6. On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Which linear inequality is represented by the graph?
- Since the line is solid, it represents an "equal to" situation as well.
- Everything to the right is shaded, indicating:
**y ≥ One-halfx + 2.**
### 7. Which points are solutions to the linear inequality \( y < 0.5x + 2 \)? (Select three options.)
- Evaluate each point:
- (–3, –2): LHS = -2, RHS = 0.5*(-3)+2 = 0.5. Yes.
- (–2, 1): LHS = 1, RHS = 0.5*(-2)+2 = 1. No.
- (–1, –2): LHS = -2, RHS = 0.5*(-1)+2 = 1. Yes.
- (–1, 2): LHS = 2, RHS = 0.5*(-1)+2 = 1. No.
- (1, –2): LHS = -2, RHS = 0.5*(1)+2 = 2. No.
- Thus, the solutions are:
**(–3, –2), (–1, –2)**.
### 8. Which is the graph of the linear inequality \( 2y > x - 2 \)?
- The line is dashed indicating strict inequality.
- Everything above the line represents:
**On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything above the line is shaded.**
### 9. Which linear inequality is represented by the graph?
- Solid line indicates ≤ or ≥, everything above indicates:
**y ≥ One-thirdx - 1.**
### 10. Which point is a solution to the inequality \( y ≤ -x + 1 \)?
- Evaluate the points:
- (2, 3): LHS = 3, RHS = -2. No.
- (3, –2): LHS = -2, RHS = -2. Yes (on the boundary).
- (2, 1): LHS = 1, RHS = -1. No.
- (–1, 3): LHS = 3, RHS = 2. No.
- Thus, the solution is:
**(3, –2).**
Feel free to ask if you have any further questions!
Answer
for 1 4 and 8 what graph number? so like i mentioned 4 graphs each question or more than 1 i give the transcript and you separate the each transcripts i did not title graph 1 2 3 or 4 so tell me the answer as in graph number please
Answered by
GPT-4o mini
Sure! Based on the descriptions given in your first message, here are the answers to which graph number corresponds to each of the specified problems:
### 1. Which is the graph of the linear inequality \( y < 3x + 1 \)?
- **Graph Number: 3** (Dashed line with positive slope, below the line is shaded.)
### 4. Which is the graph of the linear inequality \( 2x - 3y < 12 \)?
- **Graph Number: 3** (Dashed line with positive slope, below the line is shaded.)
### 8. Which is the graph of the linear inequality \( 2y > x - 2 \)?
- **Graph Number: 4** (Dashed line with positive slope, above the line is shaded.)
Let me know if you need further clarification or anything else!
### 1. Which is the graph of the linear inequality \( y < 3x + 1 \)?
- **Graph Number: 3** (Dashed line with positive slope, below the line is shaded.)
### 4. Which is the graph of the linear inequality \( 2x - 3y < 12 \)?
- **Graph Number: 3** (Dashed line with positive slope, below the line is shaded.)
### 8. Which is the graph of the linear inequality \( 2y > x - 2 \)?
- **Graph Number: 4** (Dashed line with positive slope, above the line is shaded.)
Let me know if you need further clarification or anything else!