| OK, maybe we don't have an equation | ||
| we just have two points. | ||
| And we want to know what equation line | ||
| goes through both of them. | ||
| Maybe we have the points X = 1, Y = 2 (1,2) | ||
| and the point X = 5, Y = 3 (5,3). | ||
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| We want to figure out what equation | ||
| has a graph line that goes through these two points. | ||
| How do we do it? | ||
| Well we know that when we DO figure out | ||
| what the equation is, | ||
| these two points will be part of it. | ||
| We can use these two points to figure out | ||
| what the slope of the line is. | ||
| Remember ... | ||
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| So: | ||
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| The slope is 1/4. | ||
| That means when we do find the equation | ||
| that goes through the two points, | ||
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it will look like this ... |
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| But what is the something? | ||
| Here's how we find out ... | ||
| Choose either one of the points | ||
| as the values X1 and Y1 | ||
| and use the formula ... | ||
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| Let's chose the point where X = 1 and Y = 2 ... | ||
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| Multiply out the right side ... | ||
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| Add 2 to each side to get | ||
| Y by itself on the left side ... | ||
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| The equation line that goes through | ||
| both of our points is ... | ||
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| Let's look at that formula again. | ||
| When we have any point and the slope of the line | ||
| the equation for the line can be found using ... | ||
|
Y - Y1 = m(X - X1) |
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| and we can find the m (the slope) | ||
| if we know any two points on the line ... | ||
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| If we really want something that looks impressive, | ||
| we can put the formula for finding the slope | ||
| into the formula for finding the line. | ||
| We would get ... | ||
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| That last equation is called: | ||
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The Two Point Equation of a Line |
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| Ya know, I'm glad we're done with that. | ||
| That was a ton of stuff about two points. | ||
| I bet there's not one more thing | ||
| we could do with two points! | ||
| Then again ... | ||
|
copyright 2005 Bruce Kirkpatrick |
