MHB Point on Graph of Equation....2

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The discussion confirms that the point (a - 1, a + 1) lies on the graph of the equation y = x + 2. By substituting x with a - 1, the resulting y value matches the original point's y coordinate, a + 1. The calculations demonstrate that both sides of the equation are equal, validating the point's position on the graph. Thus, it is concluded that the point indeed lies on the graph of the equation. The verification process is accurate and supports the conclusion.
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Determine if the given point lies on the graph of the equation.

(a - 1, a + 1); y = x + 2

Let x = a - 1

Let y = a + 1

y = x + 2

a + 1 = a - 1 + 2

a + 1 = a + 1

Yes, the given point lies on the graph of y = x + 2.

Correct?
 
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Checking:

y = x + 2

Let x = a - 1

y = a - 1 + 2

y = a + 1

After plugging x = a - 1 into the linear equation y = x + 2, I found the original value of y given in the point. So, I conclude that the point (a - 1, a + 1) lies on the graph of the equation.

Correct?
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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