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daveydickler daveydickler
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11 years ago
How do I find the slope between these two points? (2,3) and (2, -10)
 Please explain as much in detail as you can! Math is not my forte!

 Bonus question: when is a converse of a statement false? And what do p and q stand for on a truth table?
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wrote...
11 years ago
Take the difference in the y coordinates, divided by the difference in the x coordinates.
Be sure to take them in the same orders.  If the points are (x1, y1) and (x2, y2), the slope is
(y2 - y1) / (x2 - x1).  Sometimes this is described as "rise over run" -- how much did the line go up, and how long a distance (on the x-axis) did it have to run to get there.

You have (3-10) / (2-2).  Hmm, -7 / 0.  That can't be calculated since you can't divide by 0.  This would be a good situation where you could call this "infinity" (not actually a number, so that's a mathematically loose statement), and say that the line between the two points has infinite slope.  The line is vertical, so slope is infinite, or undefined.

P and Q in a truth table are just symbols for propositions.

When is a converse of a statement false?  Can't really answer that.  If the statements are:
P: Even numbers are multiples of 2.
Q. Even numbers are divisible evenly by 2.

The P==>Q is true, and the inverse, Q==>P is also true.
We can say P if and only if Q.

But sometimes the inverse is not true.
P: I'm going to spend a lot of time on the beach in Florida this summer.
Q. I'm going to get a tan this summer.

P==>Q is true, but Q does not imply P.  For example, maybe I'll be going to Hawaii this summer instead of Florida, or just using a UV tanning bed (in spite of the risks!)

Maybe the answer you are looking for is that the inverse of a statement is true only when the statement and its inverse are equivalent.  That's pretty basic, and I guess it's a definition for "equivalent," but it's as good an answer as any to your question.
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