To determine which statement is correct given that the point [tex]\((2,5)\)[/tex] is on the graph of an equation, let's analyze each option one by one:
A. The values [tex]\(x=2\)[/tex] and [tex]\(y=5\)[/tex] are the only values that make the equation true.
- This statement claims that the equation has no other solutions except for the point [tex]\((2, 5)\)[/tex]. However, this is often not the case with most equations, especially those that represent continuous functions. For many equations or graphs of functions, there can be multiple points that satisfy the equation. Hence, this statement is too restrictive and is likely false.
B. There are solutions to the equation for the values [tex]\(x=2\)[/tex] and [tex]\(x=5\)[/tex].
- This statement suggests that you can plug in either [tex]\(x=2\)[/tex] or [tex]\(x=5\)[/tex] into the equation and find corresponding [tex]\(y\)[/tex]-values that make the equation true. While it might be valid for some equations, it doesn't specifically confirm the role of the coordinate [tex]\((2, 5)\)[/tex]. We are focused on knowing exactly about the point [tex]\((2, 5)\)[/tex], not other coordinates like [tex]\(x=5\)[/tex], so this statement is not specific enough.
C. The values [tex]\(x=2\)[/tex] and [tex]\(y=5\)[/tex] make the equation true.
- This statement clearly asserts that substituting [tex]\(x=2\)[/tex] and [tex]\(y=5\)[/tex] into the equation will satisfy it. Since we know that the point [tex]\((2, 5)\)[/tex] is on the graph of the equation, this statement must be true. This means that when [tex]\(x = 2\)[/tex] and [tex]\(y = 5\)[/tex], they indeed make the equation true, confirming the correctness of this statement.
D. The values [tex]\(x=5\)[/tex] and [tex]\(y=2\)[/tex] make the equation true.
- This statement is suggesting that [tex]\((5, 2)\)[/tex] is a solution to the equation. There's no given information supporting that [tex]\((5, 2)\)[/tex] is a solution. We only know about the point [tex]\((2, 5)\)[/tex]. Thus, this statement is false.
Considering the analysis, the correct statement is:
C. The values [tex]\(x=2\)[/tex] and [tex]\(y=5\)[/tex] make the equation true.
Hence, the correct answer is:
Option C.
