MHB How Do I Find a Point on a Curve with a Specific Slope?

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To find a point P on the curve y = sqrt{x} where the slope of the line through P and (1, 1) is 1/4, use the slope formula with the points (1, 1) and (x, sqrt{x}). The slope formula is (sqrt{x} - 1) / (x - 1) = 1/4. Solving this equation will yield the specific x-coordinate for point P. The slope-intercept formula is not necessary for this problem. The focus should remain on applying the slope formula correctly to determine the desired point on the curve.
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Find a point P on the curve y = sqrt{x} such that the slope of the line through P and (1, 1) is 1/4.

Must I use the slope-intercept formula here?
 
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RTCNTC said:
Find a point P on the curve y = sqrt{x} such that the slope of the line through P and (1, 1) is 1/4.

Must I use the slope-intercept formula here?

Just the slope formula, with the points (1, 1) and $\displaystyle \begin{align*} \left( x, \sqrt{x} \right) \end{align*}$.
 
Prove It said:
Just the slope formula, with the points (1, 1) and $\displaystyle \begin{align*} \left( x, \sqrt{x} \right) \end{align*}$.

I can take it from here.
 

Thread 'Area of Overlapping Squares'

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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