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Question 3 of 20 If the point \( (2,5) \) is on the graph of an equation, which statement must be true? A. There are solutions to the equation for the values \( x=2 \) and \( x=5 \). B. The values \( x=2 \) and \( y=5 \) are the only values that make the equation true. C. The values \( x=2 \) and \( y=5 \) make the equation true. D. The values \( x=5 \) and \( y=2 \) make the equation true.

Ask by Whittaker Bolton. in the United States
Feb 04,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The values \( x=2 \) and \( y=5 \) make the equation true.

Solution

The correct answer is: **C. The values \( x=2 \) and \( y=5 \) make the equation true.** **Explanation:** When a point \((2, 5)\) is on the graph of an equation, it means that when \(x = 2\) and \(y = 5\), the equation holds true. This does not necessarily imply that \(x = 5\) or \(y = 2\) would also satisfy the equation, nor does it indicate that these are the only values that satisfy the equation. It simply confirms that \(x = 2\) and \(y = 5\) are specific solutions to the equation. **Why Other Options Are Incorrect:** - **A.** This statement incorrectly suggests that both \(x=2\) and \(x=5\) are solutions independently, which isn't necessarily true. - **B.** This implies that \(x=2\) and \(y=5\) are the only solutions, which is not necessarily the case. - **D.** This swaps the \(x\) and \(y\) values, which doesn't hold true unless the equation is symmetric in \(x\) and \(y\), which is not specified. **Final Answer:** C. The values \( x=2 \) and \( y=5 \) make the equation true.

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The Deep Dive

If the point \( (2,5) \) is on the graph of an equation, it means exactly that when \( x=2 \), the equation outputs \( y=5 \). This is like finding the secret treasure on a map; it confirms that you've hit the jackpot at those coordinates! When evaluating the options, it's clear that option C is the shining star! It correctly states that the values \( x=2 \) and \( y=5 \) make the equation true, affirming the relationship between \( x \) and \( y \) at this specific point on the graph. Keep that treasure map handy, and always follow those coordinates!

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