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

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SUMMARY

The discussion focuses on finding a point P on the curve defined by the equation y = sqrt{x} such that the slope of the line connecting point P and the fixed point (1, 1) equals 1/4. Participants confirm that the slope formula, rather than the slope-intercept formula, is the appropriate method to use. The slope formula is applied using the coordinates (1, 1) and (x, sqrt{x}), leading to the conclusion that the correct approach involves setting up the slope equation and solving for x.

PREREQUISITES
  • Understanding of slope formula in coordinate geometry
  • Familiarity with the curve y = sqrt{x}
  • Basic algebra skills for solving equations
  • Knowledge of coordinate points and their representation
NEXT STEPS
  • Practice solving slope problems using the slope formula
  • Explore the properties of the curve y = sqrt{x}
  • Learn about derivatives and their application in finding slopes of curves
  • Investigate the relationship between points on a curve and tangent lines
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in understanding the geometric interpretation of slopes on curves.

mathdad
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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.
 

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