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)
3 answers
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!
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
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!
