SOLUTION: Find the slope of the line through the pair of points. 1) (4,6) and (-2,-9)

Question 1143259: Find the slope of the line through the pair of points. 1) (4,6) and (-2,-9)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If you just want to get the answer and not know what it means, use the formula for calculating slope:

For this example,

If you want to UNDERSTAND slope (and understand why the formula works), think about the meaning of slope.

Slope is the ratio of how far you move up or down to how far you move left or right. To make it simple, you can always imagine "walking" left to right on the graph, meaning you always start at the point with the smaller x coordinate.

It's like the slope of a path you are hiking in the mountains -- it tells you how far you move up or down each time you take a step forward.

So picture (in your mind, if not on paper) walking from (-2,-9) to (4,6). You move 6 steps to the right (from -2 to +4); in doing that you move 15 steps up (from -9 to +6). The ratio is 15/6 or 5/2; that is your slope.

I have seen far too many students blindly plugging numbers into the formula for slope without understanding the meaning of the formula and getting wrong answers because they put the wrong numbers in the wrong places. Mistakes like that are far less frequent if you have a mental picture.

So if you choose to use the formula for calculating slope, at least have an idea whether the answer you get is reasonable. A quick mental picture of the two given points shows that the slope is positive and greater than 1 (you are going uphill faster than you are moving right); if your result from using the formula is negative, or a positive number less than 1, you haven't used the formula correctly.
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