Can you find the slope of a line passing through two points with this formula?

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    Line Slope
In summary, slope is the measure of a line's steepness and is calculated by dividing the change in y-coordinate by the change in x-coordinate. A positive slope indicates an increasing line from left to right, while a negative slope indicates a decreasing line. The slope of a line can be used to prove parallel or perpendicular lines by comparing their values.
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mathdad
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Show that the slope of the line passing through the two points (x, x^2) and (x + h, (x + h)^2) is 2x + h.

Let me see if I can solve this baby on my own.

Let m = slope = 2x + h

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

If I simplify the right side, it should give me m, right?

At the very end, I should have 2x + h = 2x + h.
 
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Simplify it, then ...
 
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m = [(x + h)^2 - x^2]/[(x + h) - x]

m = [x^2 + 2hx + h^2 - x^2]/h

m = (2hx + h^2)/h

m = 2x + h

Done!
 

FAQ: Can you find the slope of a line passing through two points with this formula?

What is the definition of slope?

The slope of a line is a measure of its steepness and is defined as the change in the y-coordinate over the change in the x-coordinate between any two points on the line.

How is slope calculated?

Slope is calculated by dividing the change in the y-coordinate by the change in the x-coordinate. This can be represented by the formula: slope = (y2 - y1) / (x2 - x1).

What does a positive slope indicate?

A positive slope indicates that the line is increasing from left to right, meaning that the y-coordinate is increasing as the x-coordinate increases.

What does a negative slope indicate?

A negative slope indicates that the line is decreasing from left to right, meaning that the y-coordinate is decreasing as the x-coordinate increases.

How can the slope of a line be used to prove parallel or perpendicular lines?

Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. Therefore, by calculating the slopes of two lines, we can determine if they are parallel or perpendicular.

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