Asked by julian celeste
Use the image to answer the question.
A coordinate plane shows a graph of an upward-sloping, diagonal, dashed line, with shading extending from the line to the left. The line starts in quadrant 3, extends through quadrant 4, and ends in quadrant 1.
Is the point (0,−3)
a solution to the inequality y>45x−3
, as shown on the graph?
(1 point)
Responses
Yes, because (0,−3)
falls on the boundary line.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.
No, because (0,−3)
falls on the boundary line.
No, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.
No, because (0,−3)
falls within the shaded region.
No, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.
Yes, because (0,−3)
falls within the shaded region.
A coordinate plane shows a graph of an upward-sloping, diagonal, dashed line, with shading extending from the line to the left. The line starts in quadrant 3, extends through quadrant 4, and ends in quadrant 1.
Is the point (0,−3)
a solution to the inequality y>45x−3
, as shown on the graph?
(1 point)
Responses
Yes, because (0,−3)
falls on the boundary line.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.
No, because (0,−3)
falls on the boundary line.
No, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.
No, because (0,−3)
falls within the shaded region.
No, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.
Yes, because (0,−3)
falls within the shaded region.
Answers
Answered by
GPT-4o mini
To determine whether the point \( (0, -3) \) is a solution to the inequality \( y > 45x - 3 \), we need to analyze the graph of the inequality.
1. **Understanding the Boundary Line**: The boundary line for the equation \( y = 45x - 3 \) is dashed, indicating that points on the line do not satisfy the inequality (the inequality is greater than, not greater than or equal to).
2. **Evaluating the Point**: The point \( (0, -3) \) corresponds to \( x = 0 \) and \( y = -3 \). To see if this point satisfies the inequality, we will substitute \( x = 0 \) into the equation of the boundary line:
\[
y = 45(0) - 3 \Rightarrow y = -3.
\]
Thus, the point \( (0, -3) \) lies on the boundary line.
3. **Shading**: According to the provided description, the shading extends from the line to the left. Therefore, the region to the left of the line includes points where \( y \) is less than \( 45x - 3 \).
Now that we have this information, we can conclude:
- Since \( (0, -3) \) lies on the dashed boundary line, it does not satisfy the inequality \( y > 45x - 3 \).
Therefore, the correct response is:
**No, because (0,−3) falls on the boundary line.**
1. **Understanding the Boundary Line**: The boundary line for the equation \( y = 45x - 3 \) is dashed, indicating that points on the line do not satisfy the inequality (the inequality is greater than, not greater than or equal to).
2. **Evaluating the Point**: The point \( (0, -3) \) corresponds to \( x = 0 \) and \( y = -3 \). To see if this point satisfies the inequality, we will substitute \( x = 0 \) into the equation of the boundary line:
\[
y = 45(0) - 3 \Rightarrow y = -3.
\]
Thus, the point \( (0, -3) \) lies on the boundary line.
3. **Shading**: According to the provided description, the shading extends from the line to the left. Therefore, the region to the left of the line includes points where \( y \) is less than \( 45x - 3 \).
Now that we have this information, we can conclude:
- Since \( (0, -3) \) lies on the dashed boundary line, it does not satisfy the inequality \( y > 45x - 3 \).
Therefore, the correct response is:
**No, because (0,−3) falls on the boundary line.**
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