Find the Numbers to CONTROL the GRAPH Follow the steps below
to see how changing the numbers of a linear equation can alter the look
of its graph. Check off each step as you go. |
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1 |
To begin, you will need to find a graphing calculator or a software program that will graph equations for you. If you need a program like that, you can download a 30 day trial version of EQUATION GRAPHER here. (We use this program at themathlab.com.) Each calculator and piece of software is a bit different, so experiment, read your manual, and get to know your "automatic grapher" as you complete the following steps. |
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2 | First, set your
graph ranges to create a grid on the screen that extends from -10 to +10 on BOTH the x and y axes. Also set your step or increment value to one for both axes. |
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3 |
Have your machine graph the
linear equation y = x.
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4 |
Now draw y = -x. Describe how adding the negative sign changes the original line. |
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5 | Erase the line y= -x, but leave y = x on your screen. | ||
6 |
Draw y = 2x, and then y = 5x. Describe how the numbers 2 and 5 change your original y = x graph.
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7 |
Try y = 100x. What happens? Why do you think we can't see it very well?
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8 |
Change the range values to Ymin = -5 and Ymax = 100. Describe what happens.
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9 |
Now change the domain values to Xmin = -1 and Xmax = 2. Describe what happens.
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10 | Now erase all equations except y = x, and set your range back to -10 to +10 on both axes, with a step or increment of 1. | ||
11 |
Now graph y = (1/2)x.
Be sure to use the parentheses or you will get a strange graph. You could
also use y = 0.5x. Describe how this changes from the graph of
Now graph y = 1/2x without the parentheses. Describe what the graph looks like.
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12 |
Graph y = (-1/5)x. Describe what happens to the line.
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13 |
Now graph y = (-1/100)x. Describe the graph.
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14 |
Change the range values so you can see this better. When you get it the way you like, tell us what values you used.
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15 | Clear out all lines except y = x, and reset your range to -10 to +10 on both axes with a step of 1. | ||
16 |
Graph y = x + 3 and describe how this differs from the graph of y = x.
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17 |
What similarities do you notice about these two lines; y = x and y = x + 3.
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18 |
Graph y = x - 3 and describe how it differs from y = x.
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19 |
What similarities do you notice about these three lines?
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20 |
Graph y = -x + 3 and describe this line. Be sure to mention how steep it is, if it is sloping downhill or uphill and where it crosses the y axis.
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21 |
Graph y = -x - 3 and describe this line.
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22 |
What do the lines from steps 20 and 21 have in common?
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23 |
Graph y = -x + 20. Can you see it? What can you do to see it?
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24 | Erase all lines. | ||
25 |
Graph the following lines,
and examine them closely as you do.
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26 |
Based upon your experimentation above, try to find an equation that will give you the graph below. When you find it write it in the space provided.
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27 |
Based upon your experimentation above, try to find an equation that will give you the graph below. When you find it write it in the space provided. Equation
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