| So now we can graph equations like ... | |||
|
Y = 3X - 4 |
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| without much problem. | |||
| The graph of this line has a slope of 3 (the X coefficient). | |||
| We can also see pretty easily that when X = 0, Y = -4. | |||
| With a bit more work, we can also see that | |||
| when X = 1, Y = -1 ... | |||
| Y = 3X - 4 | |||
| Y = 3(1) - 4 | |||
| Y = 3 - 4 | |||
| Y = - 1 | |||
| So we can graph this puppy ... | |||
|
|
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| This wasn't too bad, but when some people see an equation | |||
| that's only slightly different , they lose it completely. | |||
| Say something like ... | |||
|
Y > 3X - 4 |
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| This thing is no big deal. | |||
| Here's what you do with it. | |||
| STEP 1: | |||
|
Pretend it's got an equal sign and graph it. |
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| STEP 2 | |||
| Now, pick some test point on the graph that's not on the line. | |||
| and see if it makes the inequality true. | |||
| (X = 0, Y = 0 is a good one if it's not on the line) | |||
| Y > 3X - 4 | |||
| 0 > 3(0) - 4 | |||
| 0 > - 4 which is true! | |||
| If the inequality is true when we put in the test point, | |||
| then everything on the same side of the graph line | |||
| as the test point gets shaded. | |||
| If the inequality is NOT true when we put in the test point, | |||
| then everything on the OTHER SIDE of the graph line | |||
| from the test point gets shaded. | |||
|
|
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| STEP 3: | |||
| The last thing to deal with is the line itself. | |||
| If the equation uses ³ or £ then the line is solid | |||
| If it uses > or < then the line is dotted. | |||
| The solid lines mean that the points on the line | |||
| are included in the area that makes the equation true. | |||
| The dotted line means that all of the points | |||
| UP TO the points on the line on the shaded side | |||
| make the equation true. | |||
|
Y > 3X - 4 uses > |
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| so the line is dotted ... | |||
|
|
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| Let's try another one ... | |||
| Example: | |||
|
Y < X |
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| STEP 1: | |||
|
Pretend it's got an equal sign and graph it. |
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| OK, the slope = 1. When X = 0, Y = 0. When X = 2, Y = 2 ... | |||
|
|
|||
| STEP 2 | |||
| Now, pick some test point on the graph that's not on the line. | |||
| and see if it makes the inequality true. | |||
| OK, we can't use (0,0) because it's on the line | |||
| So let's try the point where X = 2 and Y = 3. | |||
|
|
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| Y < X | |||
| 3 < 2 nope, that's not true! | |||
| That means the side we shade | |||
| is the side that the point is NOT on ... | |||
|
|
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| STEP 3: | |||
| The last thing to deal with is the line itself. | |||
| If the equation uses ³ or £ then the line is solid | |||
| If it uses > or < then the line is dotted. | |||
| The equation uses the less than symbol, | |||
| so the equation has a dotted line ... | |||
|
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|
copyright 2005 Bruce Kirkpatrick |
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