Algebra 1 Calculating Slopes
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Calculating Slopes

 
 Math people wanted a really good way 
 to talk about how steep the graph line was.
 
 Let's look at an equation that we worked with 
 on the last page ...
 

 
 The way "the steepness" of the line is measured
 is pretty simple ...
 
 STEP 1:
 Choose any point on the line.
 Label the X value of that point X1
 Label the Y value of that point Y1
 
 So let's choose the point (0, -3) for this. 
 That means X1 = 0 and Y1 = -3.
 
 STEP 2:
 Choose any other point on the line.
 Label the X value of that point X2
 Label the Y value of that point Y2
 
 So choose the point (2, 1) for this one. 
 That means X2 = 2 and Y2 = 1.
 (Hey, it was the only other point we had worked out!)
 
 STEP 3:
 Take the 4 values and put them into this formula ...
 

 
 and find the answer ...
 

 
 So the slope of the equation Y = 2X - 3 is 2.
 
 Math people sometimes call the slope of an equation "m"
 (who knows why).
 
 So we say that for the equation Y = 2X - 3, that m = 2.
 
 The slope actually tells us 
 how many units the line goes up (+) or down (-)
 for each unit it goes from left to right.
 
 The amount the line goes up
 is how much bigger Y gets.
 
 The amount the line moves to the right
 is how much bigger X gets.
 
 Getting bigger (or smaller) is a change.
 Another little code that you may see
 in math or science is a triangle "D"
 This triangle has a name.
 It is called delta.
 
 The slope is the amount that Y changes,
 divided by the amount that X changes.
 This is sometimes written as ...
 

 
 Did you notice in the equation that the number 
 next to X term was 2, and so was the slope?
 
 Did you think that was just luck?
 NOPE!
 
 Whenever the equation is set up like ...
 

Y = (some number)X + (some other number)

 
 The number next to the X term (it's coefficient) 
 is the slope.
 
 Not only that, the "(some other number)" is the Y value
 where the equation line crosses the Y number line (axis).
 
 SO, in the equation ...
 

 
 The larger the slope number is,
 the faster the line goes up from left to right ...
 

 
 We say that the equation with the slope of 2
 is STEEPER than the equation with the slope of 1.
 
 If the number next to the X is negative,
 the equation line goes down from left to right ...
 

 
 If two equation lines have the same slope,
 they have equation lines that are parallel
 or are the same line ...
 

 
 But if two equations don't have the same slope,
 their equation lines MUST cross somewhere.
 

   copyright 2005 Bruce Kirkpatrick

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