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

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In summary, the conversation discusses proving that the slope of a line passing through the points (x, x^2) and (x + h, (x + h)^2) is equal to 2x + h. The conversation uses algebraic equations to show that the slope is indeed equal to 2x + h.
  • #1
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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  • #2
Let's assume that it is not correct. Where is the error?
 
  • #3
greg1313 said:
Let's assume that it is not correct. Where is the error?

I do not understand.
 
  • #4
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!
 

1. What is the slope of a line?

The slope of a line is a measure of its steepness or incline. It represents the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line.

2. How do you find the slope of a line?

To find the slope of a line, you can use the slope formula, which is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. Alternatively, you can count the rise (vertical change) over the run (horizontal change) between two points on the line.

3. What does a positive slope indicate?

A positive slope indicates that the line is increasing from left to right. This means that as the x-coordinate increases, the y-coordinate also increases. In other words, the line is moving upwards.

4. What does a negative slope indicate?

A negative slope indicates that the line is decreasing from left to right. This means that as the x-coordinate increases, the y-coordinate decreases. In other words, the line is moving downwards.

5. Can the slope of a line be zero?

Yes, the slope of a line can be zero. This indicates that the line is horizontal and has no incline. In this case, the y-coordinate remains the same regardless of the change in the x-coordinate.

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