Question
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 within the shaded region.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.
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 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.
(1 point)
Responses
Yes, because (0,−3) falls within the shaded region.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.
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 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.
Answers
GPT-4o mini
To determine if the point (0, -3) is a solution to the inequality \( y > 45x - 3 \), we first need to consider the boundary line described by the equation \( y = 45x - 3 \).
1. **Calculate the value of \( y \) at \( x = 0 \)**:
\[
y = 45(0) - 3 = -3
\]
So, the point (0, -3) lies on the boundary line.
2. **Analyze the inequality**:
The inequality \( y > 45x - 3 \) means that we are looking for points where the \( y \)-value is greater than the \( y \)-value given by the line \( y = 45x - 3 \). Since (0, -3) is on the boundary line, it does not satisfy the inequality (it is equal to the boundary value, not greater).
Thus, the correct response is:
**No, because (0,−3) falls on the boundary line.**
1. **Calculate the value of \( y \) at \( x = 0 \)**:
\[
y = 45(0) - 3 = -3
\]
So, the point (0, -3) lies on the boundary line.
2. **Analyze the inequality**:
The inequality \( y > 45x - 3 \) means that we are looking for points where the \( y \)-value is greater than the \( y \)-value given by the line \( y = 45x - 3 \). Since (0, -3) is on the boundary line, it does not satisfy the inequality (it is equal to the boundary value, not greater).
Thus, the correct response is:
**No, because (0,−3) falls on the boundary line.**