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Question 1200209: Find the slope of the line (-2,2) and (4,-1)
Found 4 solutions by josgarithmetic, ikleyn, math_tutor2020, greenestamps:
Answer by josgarithmetic(39630)   (Show Source):
Answer by ikleyn(52915)  (Show Source):
Answer by math_tutor2020(3817) (Show Source):
Answer by greenestamps(13216)  (Show Source):
You can put this solution on YOUR website!
You have three responses, all of which say "use the formula"; and that is what nearly all references tell you to do.
It's my belief that you will enjoy math more if you understand what you are doing, instead of plugging numbers into a formula.
I have seen far too many cases where a student tries to use the slope formula and puts the wrong numbers in the wrong places, getting the wrong answer. And if I myself used the formula a hundred times to find the slope determined by two points, I would probably get the wrong answer one or two times, due to carelessness.
My suggestion to you is to use the following "rise over run" definition: the ratio of how far I go up or down to how far I go TO THE RIGHT.
Note I arbitrarily choose to move to the right, so that the "run" is positive, eliminating the possible need to divide by a negative number.
In this example, I would first look at the two x coordinates to see -2 and 4, so I will be moving from the first given point to the second. Then the run is from -2 to 4, a change of 6; and when I move 6 to the right, the change in y is from 2 to -1, a change of -3. And so the ratio of rise to run is -3/6 = -1/2.
ANSWER: -1/2
Of course, that is the calculation you will do if you use the slope formula CORRECTLY....
But I believe you will make fewer careless mistakes if you do the calculation the way I described, rather than by using the formula.
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