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

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The discussion centers on demonstrating that the slope of the line through the points (x, x^2) and (x + h, (x + h)^2) equals 2x + h. The slope is calculated using the formula m = [(x + h)^2 - x^2] / (x + h - x). Through algebraic manipulation, it is shown that both sides of the equation simplify to 2x + h. The conclusion confirms that the initial assumption about the slope being equal to 2x + h is correct. The proof is successfully completed.
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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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