| OK, up to now this X Y graphing hasn't been too exciting | |||
| or too valuable, but here's the payoff. | |||
| When we have an equation with just X's and Y's, | |||
| that is, no exponents in the equation (like X 3 or anything) | |||
| all of the X = this and Y = that solutions to the equation | |||
| will be on a straight line on the graph! | |||
| Once we have 2 points, we just draw the line that goes between them | |||
| to get all of the possible X = this and Y = that | |||
| solutions to the problem. | |||
| The line (and the answers) go on in both directions forever. | |||
| To show this, we always draw arrow heads | |||
| at the ends of the lines. | |||
| So we can take the graph from the last page ... | |||
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| and do this! | |||
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| Let's do another one ... | |||
| Example: | |||
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-X + 4 = Y |
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| For the first X point, chose X = 0. | |||
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It's usually the easiest one to do. |
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-X + 4 = Y |
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| -(0) + 4 = Y | |||
| 4 = Y | |||
| So we have X = 0, Y = 4. | |||
| Mark it on the graph ... | |||
| Did you notice that whenever X = 0 | |||
| the point is on the Y number line (Y axis)? | |||
| Also if Y = 0 for a point | |||
| it will be on the X axis. | |||
| So we need one more point. | |||
| Let's try X = 2 ... | |||
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-X + 4 = Y |
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| -(2) + 4 = Y | |||
| 2 = Y | |||
| So we have X = 2, Y = 2. | |||
| Draw in that point ... | |||
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| Now with 2 points, we can draw in the line | |||
| that all the X = this and Y = that points are on ... | |||
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| In the first example, the line was going up | |||
| as it went from left to right. | |||
| In this one, the line is going down | |||
| as it goes from left to right. | |||
| It sort of looks like the side of a hill | |||
| OR A SKI SLOPE. | |||
| Math people decided to call this "going up" | |||
| and "going down" thing the SLOPE of the line. | |||
| WOW! A name that makes sense! Amazing. | |||
| The names that other parts of the graph get | |||
| are harder to remember. | |||
| The number lines themselves are called AXIS. | |||
| The X number line is the X AXIS. | |||
| The Y number line is the Y AXIS. | |||
| The X and Y value pair numbers are called COORDINATES. | |||
| The point where the X and Y number lines cross | |||
| is called the ORIGIN. | |||
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copyright 2005 Bruce Kirkpatrick |
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