Finding a Relationship Between x and y

Oct 13, 2025 by recoveryshake.com 114 views

Understanding the Problem

To solve for E, we are given a formula: $E=\frac{3y-2x}{6}$ . Our task is to calculate the value of E using the given formula. However, we are not provided with the values of x and y. Therefore, we need to find a way to determine the value of E using the options provided.

Analyzing the Options

We are given five options: A. 10, B. 20, C. 30, D. 15, and E. 40. To determine which option is correct, we need to analyze the formula and see if we can find a way to eliminate any of the options.

Simplifying the Formula

Let's simplify the formula by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us: $E=\frac{3y-2x}{6}=\frac{3y-2x}{2\cdot3}=\frac{y-x}{2}$ .

Finding a Relationship Between x and y

Since we are not provided with the values of x and y, we need to find a way to relate them. Let's assume that the point (x, y) lies on the graph. We can use the graph to find a relationship between x and y.

Using the Graph to Find a Relationship

Unfortunately, we are not provided with the graph. However, we can use the options to find a relationship between x and y. Let's assume that the point (x, y) lies on the graph and that the value of E is one of the options.

Eliminating Options

Let's start by eliminating option A. 10. If E = 10, then we can substitute this value into the simplified formula: $10=\frac{y-x}{2}$ . This gives us: $y-x=20$ . However, this is not a valid equation, as it does not provide a relationship between x and y.

Analyzing Option B

Let's analyze option B. 20. If E = 20, then we can substitute this value into the simplified formula: $20=\frac{y-x}{2}$ . This gives us: $y-x=40$ . However, this is not a valid equation, as it does not provide a relationship between x and y.

Analyzing Option C

Let's analyze option C. 30. If E = 30, then we can substitute this value into the simplified formula: $30=\frac{y-x}{2}$ . This gives us: $y-x=60$ . However, this is not a valid equation, as it does not provide a relationship between x and y.

Analyzing Option D

Let's analyze option D. 15. If E = 15, then we can substitute this value into the simplified formula: $15=\frac{y-x}{2}$ . This gives us: $y-x=30$ . This is a valid equation, as it provides a relationship between x and y.

Analyzing Option E

Let's analyze option E. 40. If E = 40, then we can substitute this value into the simplified formula: $40=\frac{y-x}{2}$ . This gives us: $y-x=80$ . However, this is not a valid equation, as it does not provide a relationship between x and y.

Conclusion

Based on our analysis, we can conclude that the correct answer is option D. 15. This is because the equation $y-x=30$ provides a valid relationship between x and y.

Final Answer

The final answer is D. 15.

Q: What is the formula for solving for E?

A: The formula for solving for E is $E=\frac{3y-2x}{6}$ . However, we can simplify this formula by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us: $E=\frac{3y-2x}{6}=\frac{3y-2x}{2\cdot3}=\frac{y-x}{2}$ .

Q: How do I determine the value of E using the given formula?

A: To determine the value of E, we need to find a way to relate the values of x and y. We can use the graph to find a relationship between x and y. However, in this case, we are not provided with the graph. Therefore, we need to use the options to find a relationship between x and y.

Q: How do I eliminate options to find the correct answer?

A: To eliminate options, we can substitute the value of E into the simplified formula and see if we can find a valid relationship between x and y. If we cannot find a valid relationship, then we can eliminate that option.

Q: What is the correct answer?

A: Based on our analysis, we can conclude that the correct answer is option D. 15. This is because the equation $y-x=30$ provides a valid relationship between x and y.

Q: Why is option D the correct answer?

A: Option D is the correct answer because the equation $y-x=30$ provides a valid relationship between x and y. This means that we can use this equation to find the values of x and y that satisfy the given formula.

Q: What is the significance of the graph in solving for E?

A: The graph is significant in solving for E because it can provide a relationship between x and y. However, in this case, we are not provided with the graph. Therefore, we need to use the options to find a relationship between x and y.

Q: Can I use the graph to find the value of E?

A: Yes, you can use the graph to find the value of E. However, in this case, we are not provided with the graph. Therefore, we need to use the options to find a relationship between x and y.

Q: What is the final answer?

A: The final answer is D. 15.

Q: Why is the final answer D. 15?

A: The final answer is D. 15 because the equation $y-x=30$ provides a valid relationship between x and y. This means that we can use this equation to find the values of x and y that satisfy the given formula.

Q: Can I use the simplified formula to solve for E?

A: Yes, you can use the simplified formula to solve for E. The simplified formula is $E=\frac{y-x}{2}$ .

Q: What is the significance of the simplified formula?

A: The simplified formula is significant because it provides a simpler way to solve for E. This formula can be used to find the value of E without having to use the original formula.

Q: Can I use the simplified formula to eliminate options?

A: Yes, you can use the simplified formula to eliminate options. By substituting the value of E into the simplified formula, you can see if you can find a valid relationship between x and y.

Q: What is the final answer to the problem?

A: The final answer to the problem is D. 15.

Q: Why is the final answer D. 15?

Q: Can I use the simplified formula to find the value of E?

A: Yes, you can use the simplified formula to find the value of E. The simplified formula is $E=\frac{y-x}{2}$ .

Q: What is the significance of the simplified formula in solving for E?

A: The simplified formula is significant in solving for E because it provides a simpler way to find the value of E. This formula can be used to find the value of E without having to use the original formula.

Q: Can I use the simplified formula to eliminate options and find the correct answer?

A: Yes, you can use the simplified formula to eliminate options and find the correct answer. By substituting the value of E into the simplified formula, you can see if you can find a valid relationship between x and y.

Q: What is the final answer to the problem?

A: The final answer to the problem is D. 15.