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

[mathdad]

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?

 

[Greg]

Let's assume that it is not correct. Where is the error?

 

[mathdad]

Let's assume that it is not correct. Where is the error?

I do not understand.

 

[mathdad]

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!