Wednesday, March 23, 2016

And Now, Vince's Uncle Roberto On How To Find the Slope of a Line from Two Points

To find the slope, we will need two points from the line.Pick two x's and solve for each corresponding y: If, say, x = 3, then y = ( 2/3 )(3) – 4 = 2 – 4 = –2. If, say, x = 9, then y = ( 2/3 )(9) – 4 = 6 – 4 = 2. (By the way, I picked the x-values to be multiples of three because of the fraction. It's not a rule that you have to do that, but it's a helpful technique.) So the two points (3, –2) and (9, 2) are on the line y = ( 2/3 )x – 4.To find the slope, you use the following formula:
    slope formula: m = [y1 - y2] / [x1 - x2]
The subscripts merely indicate that you have a "first" point (whose coordinates are subscripted with a "1") and a "second" point (whose coordinates are subscripted with a "2"); that is, the subscripts indicate nothing more than the fact that you have two points to work with. It is entirely up to you which point you label as "first" and which you label as "second". For computing slopes with the slope formula, the important thing is that you subtract the x's and y's in the same order. For our two points, if we choose (3, –2) to be the "first" point, then we get the following:

    slope calculation: m = 2/3

The first y-value above, the –2, was taken from the point (3, –2) ; the second y-value, the 2, came from the point (9, 2); the x-values 3 and 9 were taken from the two points in the same order. If we had taken the coordinates from the points in the opposite order, the result would have been exactly the same value:

    slope calculation: m = 2/3
As you can see, the order in which you list the points really doesn't matter, as long as you subtract the x-values in the same order as you subtracted the y-values. Because of this, the slope formula can be written as it is above, or alternatively it can be written as:

slope: another version of the formula 

Let me emphasize: it does not matter which of the two formulas you use or which point you pick to be "first" and which you pick to be "second". The only thing that matters is that you subtract your x-values in the same order as you had subtracted your y-values.

And speaking of values, I have driven my town car for the rudest, most reprehensible 14 year olds I have ever met. And guess what. Yes, their parents were wealthy. Don't spoil your kids with too much money, folks.

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