Does The Point { (1,7)$}$ Make The Inequality { Y \ \textgreater \ 2x + 5$}$ True?A. Yes B. No
Introduction
In mathematics, inequalities are used to compare the values of two or more expressions. They are an essential part of algebra and are used to solve equations, graph functions, and make conclusions about the relationships between variables. In this article, we will explore whether the point (1,7) makes the inequality y > 2x + 5 true.
Understanding the Inequality
The given inequality is y > 2x + 5. This means that for any value of x, the corresponding value of y must be greater than 2x + 5. In other words, the graph of the inequality y > 2x + 5 is a region above the line y = 2x + 5.
The Point (1,7)
The point (1,7) is a specific point in the coordinate plane. To determine whether this point makes the inequality true, we need to substitute the values of x and y into the inequality and see if it holds.
Substituting the Values
Let's substitute x = 1 and y = 7 into the inequality y > 2x + 5.
y > 2x + 5 7 > 2(1) + 5 7 > 2 + 5 7 > 7
Conclusion
As we can see, the inequality 7 > 7 is not true. This means that the point (1,7) does not make the inequality y > 2x + 5 true.
Why the Point Does Not Make the Inequality True
The point (1,7) lies on the line y = 2x + 5, which is the boundary of the inequality y > 2x + 5. Since the point lies on the boundary, it does not satisfy the inequality. In other words, the point (1,7) is not in the region above the line y = 2x + 5, which is the region where the inequality y > 2x + 5 is true.
Graphical Representation
To visualize the situation, let's graph the line y = 2x + 5 and the point (1,7) on the same coordinate plane.
+---------------+
| |
| y = 2x + 5 |
| |
+---------------+
| (1,7) |
+---------------+
As we can see, the point (1,7) lies on the line y = 2x + 5, which is the boundary of the inequality y > 2x + 5. This means that the point does not make the inequality true.
Conclusion
In conclusion, the point (1,7) does not make the inequality y > 2x + 5 true. This is because the point lies on the boundary of the inequality, which is the line y = 2x + 5. To make the inequality true, the point must lie in the region above the line y = 2x + 5.
Final Answer
The final answer is B. No, the point (1,7) does not make the inequality y > 2x + 5 true.
Introduction
In our previous article, we explored whether the point (1,7) makes the inequality y > 2x + 5 true. We concluded that the point does not make the inequality true because it lies on the boundary of the inequality, which is the line y = 2x + 5. In this article, we will answer some frequently asked questions related to this topic.
Q&A
Q1: What is the boundary of the inequality y > 2x + 5?
A1: The boundary of the inequality y > 2x + 5 is the line y = 2x + 5.
Q2: Why does the point (1,7) not make the inequality true?
A2: The point (1,7) does not make the inequality true because it lies on the boundary of the inequality, which is the line y = 2x + 5.
Q3: What is the region where the inequality y > 2x + 5 is true?
A3: The region where the inequality y > 2x + 5 is true is the region above the line y = 2x + 5.
Q4: Can a point on the boundary of the inequality make the inequality true?
A4: No, a point on the boundary of the inequality cannot make the inequality true. The point must lie in the region above the boundary to make the inequality true.
Q5: How can we determine whether a point makes the inequality true?
A5: To determine whether a point makes the inequality true, we need to substitute the values of x and y into the inequality and see if it holds.
Q6: What is the relationship between the point (1,7) and the line y = 2x + 5?
A6: The point (1,7) lies on the line y = 2x + 5.
Q7: Can we use the point (1,7) to graph the inequality y > 2x + 5?
A7: No, we cannot use the point (1,7) to graph the inequality y > 2x + 5. The point lies on the boundary of the inequality, which is the line y = 2x + 5.
Q8: What is the significance of the point (1,7) in the context of the inequality y > 2x + 5?
A8: The point (1,7) is significant because it lies on the boundary of the inequality, which is the line y = 2x + 5. This means that the point does not make the inequality true.
Conclusion
In conclusion, the point (1,7) does not make the inequality y > 2x + 5 true. This is because the point lies on the boundary of the inequality, which is the line y = 2x + 5. We hope that this Q&A article has provided you with a better understanding of the topic.
Final Answer
The final answer is B. No, the point (1,7) does not make the inequality y > 2x + 5 true.