Is the Slope of the Line Passing Through the Given Points Equal to 2x + h?

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Discussion Overview

The discussion revolves around the calculation of the slope of the line passing through the points (x, x^2) and (x + h, (x + h)^2). Participants are examining whether the slope can be expressed as 2x + h, exploring the algebraic manipulation involved in deriving this expression.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states that the slope m is given as 2x + h and seeks to verify this by showing that the right side of the slope formula equals the left side.
  • Another participant questions the correctness of the initial claim and asks where the error might be, indicating uncertainty about the derivation.
  • A subsequent participant echoes the previous question, expressing confusion about the correctness of the claim.
  • A later reply presents a step-by-step algebraic manipulation to show that the expression simplifies correctly to 2x + h, concluding with the statement "Done!"

Areas of Agreement / Disagreement

There is no clear consensus on the correctness of the initial claim, as some participants express doubt while others provide a derivation that supports it. The discussion remains unresolved regarding the validity of the slope expression.

Contextual Notes

The discussion includes algebraic manipulations that may depend on specific assumptions about the variables involved, and there are unresolved questions about the correctness of the initial claim.

mathdad
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Show that the slope of the line passing through the points
(x, x^2) and (x + h, (x + h)^2) is 2x + h.

Let m = slope

The slope m is given to be 2x + h.

2x + h = [(x + h)^2 - x^2)/(x + h - x)]

I must show that the right side = the left side.

Correct?
 
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Let's assume that it is not correct. Where is the error?
 
greg1313 said:
Let's assume that it is not correct. Where is the error?

I do not understand.
 
2x + h = {x+h}^{2} - {x}^{2}/(x + h - x)

2x + h = (x + h)(x + h) - {x}^{2}/h

2x + h = {x}^{2} + 2xh + {h}^{2} - {x}^{2}/h

2x + h = 2xh + {h}^{2}/h

2x + h = 2x + h

Done!
 

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