Question
Does the graph represent the solution set of the system of inequalities?
y≥2x
y≥x−2
Use the image to answer the question.
The coordinate grid has x and y axes labeled from negative 5 to 5.
Select the correct answers from the lists.
(2 points)
The nonlinear graph should be a solid exponential function that approaches zero as x approaches negative infinity, and approaches infinity as x approaches infinity with shading
it.
The line should be a
line, with a slope of 1, a y-intercept of −2
, with shading
it.
So, the graph
represent the solution set of the system of inequalities.
Remaining Attempts : 3
y≥2x
y≥x−2
Use the image to answer the question.
The coordinate grid has x and y axes labeled from negative 5 to 5.
Select the correct answers from the lists.
(2 points)
The nonlinear graph should be a solid exponential function that approaches zero as x approaches negative infinity, and approaches infinity as x approaches infinity with shading
it.
The line should be a
line, with a slope of 1, a y-intercept of −2
, with shading
it.
So, the graph
represent the solution set of the system of inequalities.
Remaining Attempts : 3
Answers
GPT-4o mini
To determine if the graph represents the solution set of the given system of inequalities \( y \geq 2x \) and \( y \geq x - 2 \), let’s analyze each inequality:
1. **For the inequality \( y \geq 2x \)**:
- The line represented by \( y = 2x \) has a slope of 2 and a y-intercept of 0.
- Since this is a "greater than or equal to" inequality, the area above this line (including the line itself) should be shaded.
2. **For the inequality \( y \geq x - 2 \)**:
- The line represented by \( y = x - 2 \) has a slope of 1 and a y-intercept of -2.
- Similar to the previous inequality, the area above this line (including the line itself) should be shaded.
In summary:
- **The first line** (\( y = 2x \)):
- It should be a **solid line** (since it's "greater than or equal to").
- It has a **slope of 2** and a **y-intercept of 0**.
- The area above the line should be shaded.
- **The second line** (\( y = x - 2 \)):
- It should also be a **solid line** (similarly "greater than or equal to").
- It has a **slope of 1** and a **y-intercept of -2**.
- The area above this line should be shaded.
Now, addressing your answer choices:
- The description you provided with the non-linear solid exponential function seems misplaced, since you are working with linear inequalities.
- For the second line, it should be stated explicitly as a **solid line**, with the proper slope and y-intercept mentioned.
So, the answers for your selections would be:
1. The first graph (associated with \( y = 2x \)):
- "The line should be a **solid line**, with a **slope of 2**, a **y-intercept of 0**, with shading **above it**."
2. The second graph (associated with \( y = x - 2 \)):
- "The line should be a **solid line**, with a **slope of 1**, a **y-intercept of -2**, with shading **above it**."
Finally:
- The graph **does represent** the solution set of the system of inequalities as long as it fulfills the conditions mentioned above (solidity of lines and correct shading direction).
So the filled-out statement should read:
"So, the graph **does** represent the solution set of the system of inequalities."
1. **For the inequality \( y \geq 2x \)**:
- The line represented by \( y = 2x \) has a slope of 2 and a y-intercept of 0.
- Since this is a "greater than or equal to" inequality, the area above this line (including the line itself) should be shaded.
2. **For the inequality \( y \geq x - 2 \)**:
- The line represented by \( y = x - 2 \) has a slope of 1 and a y-intercept of -2.
- Similar to the previous inequality, the area above this line (including the line itself) should be shaded.
In summary:
- **The first line** (\( y = 2x \)):
- It should be a **solid line** (since it's "greater than or equal to").
- It has a **slope of 2** and a **y-intercept of 0**.
- The area above the line should be shaded.
- **The second line** (\( y = x - 2 \)):
- It should also be a **solid line** (similarly "greater than or equal to").
- It has a **slope of 1** and a **y-intercept of -2**.
- The area above this line should be shaded.
Now, addressing your answer choices:
- The description you provided with the non-linear solid exponential function seems misplaced, since you are working with linear inequalities.
- For the second line, it should be stated explicitly as a **solid line**, with the proper slope and y-intercept mentioned.
So, the answers for your selections would be:
1. The first graph (associated with \( y = 2x \)):
- "The line should be a **solid line**, with a **slope of 2**, a **y-intercept of 0**, with shading **above it**."
2. The second graph (associated with \( y = x - 2 \)):
- "The line should be a **solid line**, with a **slope of 1**, a **y-intercept of -2**, with shading **above it**."
Finally:
- The graph **does represent** the solution set of the system of inequalities as long as it fulfills the conditions mentioned above (solidity of lines and correct shading direction).
So the filled-out statement should read:
"So, the graph **does** represent the solution set of the system of inequalities."