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# Explanation of slope.

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Once you have the graph of a line, how can you find its slope?

Does it matter which points you choose to find the slope?

Does the slope vary depending on your choice of points?

https://brainmass.com/math/graphs-and-functions/explanation-slope-251008

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Question : Once you have the graph of a line, how can you find its slope?

Once you have the graph of a line, you can find it slope by choosing any 2 points on the line.
The slope of a line measures the steepness of the line. So, once you select any 2 points on the graph, you can find its slope by using the following formula:
Slope = (y2 - y1)/(x2-x1). In the below given graph, you can choose any 2 points to find the slope. And the slope will always be equal.

Question : Does it matter which points you choose to find the slope?
It does not matter which points on the line you choose to find the slope, the slope will always be the same. Like in the above example...
(x1, y1) = (5, 2)
(x2, y2) = (2, 0). These 2 are the points on the positive region of the graph.
Now, let us find the slope -
Slope = (y2 - y1)/(x2-x1)
Slope = (0 - 2)/(2 - 5)
Slope = -2/-3 = 2/3.

Now let us take the points below the horizontal, that is in the negative region -
(x1, y1) = (-1, -2)
(x2, y2) = (-4, -4). These 2 are the points on the positive region of the graph.
Now, let us find the slope -
Slope = (y2 - y1)/(x2-x1)
Slope = (-4 + 2)/(-4 + 1)
Slope = -2/-3 = 2/3.

Hence we can say that the points we chose on the line does not change the slope of the line.

Question : Does the slope vary depending on your choice of points?
As explained and proved above, the slope does not vary on the choice of points by us. It always remain the same of a line.

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