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 open paren 0 comma negative 3 close paren falls within the shaded region.
No, because (0,−3)
falls on the dashed boundary line.
No, because open paren 0 comma negative 3 close paren falls on the dashed boundary line.
No, because (0,−3)
falls within the shaded region.
No, because open paren 0 comma negative 3 close paren falls within the shaded region.
Yes, because (0,−3)
falls on the boundary line.
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 open paren 0 comma negative 3 close paren falls within the shaded region.
No, because (0,−3)
falls on the dashed boundary line.
No, because open paren 0 comma negative 3 close paren falls on the dashed boundary line.
No, because (0,−3)
falls within the shaded region.
No, because open paren 0 comma negative 3 close paren falls within the shaded region.
Yes, 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 need to first understand the inequality and then evaluate the point.
1. **Substituting the Point into the Inequality:**
Substitute \(x = 0\) and \(y = -3\) into the inequality:
\[
-3 > 45(0) - 3
\]
Simplifying the right side gives:
\[
-3 > -3
\]
This statement is false because -3 is not greater than -3.
2. **Understanding the Graph:**
The inequality \(y > 45x - 3\) means the region above the line \(y = 45x - 3\). Since the line is typically represented as dashed for “greater than” (indicating that points on the line are not included in the solution), we need to analyze where (0, -3) is in relation to the line.
Given that (0, -3) is not above the line \(y = 45x - 3\)—in fact, it lies on the line itself as we determined the relationship shows that -3 equals -3 (the boundary line) and it does not meet the greater than requirement—it indicates that (0, -3) is not a part of the solution.
Therefore, the correct answer is:
**No, because (0,−3) falls on the dashed boundary line.**
1. **Substituting the Point into the Inequality:**
Substitute \(x = 0\) and \(y = -3\) into the inequality:
\[
-3 > 45(0) - 3
\]
Simplifying the right side gives:
\[
-3 > -3
\]
This statement is false because -3 is not greater than -3.
2. **Understanding the Graph:**
The inequality \(y > 45x - 3\) means the region above the line \(y = 45x - 3\). Since the line is typically represented as dashed for “greater than” (indicating that points on the line are not included in the solution), we need to analyze where (0, -3) is in relation to the line.
Given that (0, -3) is not above the line \(y = 45x - 3\)—in fact, it lies on the line itself as we determined the relationship shows that -3 equals -3 (the boundary line) and it does not meet the greater than requirement—it indicates that (0, -3) is not a part of the solution.
Therefore, the correct answer is:
**No, because (0,−3) falls on the dashed boundary line.**