Question

Which of the following points (x, y) is NOT on the graph of \(y<2x\)?

• A. (-3, -7)
• B. (3, 3)
• C. (2, -9)
• D. (2, 2)
• E. (2, 5)

Hint:

To test if a point is in the solution region of an inequality, simply plug the x and y coordinates into the inequality. If the resulting statement is true, the point is a solution. If it's false, it's not. Be careful with negative numbers and the direction of the inequality sign.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This question asks us to identify which of the given points does not satisfy the inequality \(y<2x\). A point \((x, y)\) is on the graph of an inequality if its coordinates make the inequality a true statement. We are looking for the point that makes the inequality false.
Step 2: Key Formula or Approach:
For each point \((x, y)\) given in the options, we will substitute the \(x\) and \(y\) values into the inequality \(y<2x\) and check if the resulting statement is true or false. The point that results in a false statement is the correct answer.
Step 3: Detailed Explanation:
Let's test each point:

(A) (-3, -7): Substitute \(x = -3\) and \(y = -7\). Is \( -7<2(-3) \)? Is \( -7<-6 \)? Yes, this is true. So, this point is on the graph.
(B) (3, 3): Substitute \(x = 3\) and \(y = 3\). Is \( 3<2(3) \)? Is \( 3<6 \)? Yes, this is true. So, this point is on the graph.
(C) (2, -9): Substitute \(x = 2\) and \(y = -9\). Is \( -9<2(2) \)? Is \( -9<4 \)? Yes, this is true. So, this point is on the graph.
(D) (2, 2): Substitute \(x = 2\) and \(y = 2\). Is \( 2<2(2) \)? Is \( 2<4 \)? Yes, this is true. So, this point is on the graph.
(E) (2, 5): Substitute \(x = 2\) and \(y = 5\). Is \( 5<2(2) \)? Is \( 5<4 \)? No, this is false. So, this point is NOT on the graph.
Step 4: Final Answer:
The point (2, 5) is the only one that does not satisfy the inequality \(y<2x\).