| 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 ... | ||
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| 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 ... | ||
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| and find the answer ... | ||
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| 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 ... | ||
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| 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 ... | ||
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Y = (some number)X + (some other number) |
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| 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 ... | ||
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| The larger the slope number is, | ||
| the faster the line goes up from left to right ... | ||
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| 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 ... | ||
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| If two equation lines have the same slope, | ||
| they have equation lines that are parallel | ||
| or are the same line ... | ||
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| But if two equations don't have the same slope, | ||
| their equation lines MUST cross somewhere. | ||
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copyright 2005 Bruce Kirkpatrick |
