In this section we will look at ways to work with a data table.
Isidro is playing a "guess the rule" game on the computer. He types in a number, and the computer gives a number in response. The program generates the following data set:
| x | y |
| -6 | 8 |
| -3 | 6 |
| 0 | 4 |
| 3 | 2 |
| 6 | 0 |
What is the change in the y-values from one row to the next row?
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The y-values decrease by 2 for each row. 
What is the change in the x-values from one row to the next row?
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The x-values increase by 3 for each row.
What is the ratio of the changes in y-values to the changes in x-values?
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-
-Two over 3
2
3
How does the value of y change as the value of x increases?
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The value of y decreases as the value for x increases.
Does the value of y decrease at a constant rate or at a variable rate?
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How much would the value of y change if the value of x changed by 1?
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The value of y changes by –
Two Thirds
2
3
when the value of x increases by 1.
To calculate the value of y would you multiply the value of x by ( – Two Thirds
2
3
) or add (– Two Thirds
2
3
) to the value of x?
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Multiply by – Two Thirds
2
3
What is the value of y when the value of x is 0?
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The value of y is 4 when the value of x is 0.
Use the answer to the previous question to write a new sentence that describes how the value of y relates to the value of x.
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The value of y is 4 more than (–
Two Thirds
2
3
)
times the value of x.
Write your sentence as a mathematical equation.
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y = –
Two Thirds
2
3
x + 4
Click here if you need a review of plotting points on an axis.
Click here to open a printable sheet of coordinate planes you can use to make draw graphs.
Graph the data from the table on one of the coordinate planes on the sheet you just printed.
| x | y |
| -6 | 8 |
| -3 | 6 |
| 0 | 4 |
| 3 | 2 |
| 6 | 0 |
If you need help graphing the points from the table above, you can use this
plotting applet.
ClickInteractive popup. Assistance may be required. for applet instructions.
Source: Simple Plot, Shodor
As you enter data, click the Plot/Update button after each ordered pair to see the data point appear on the graph.
ClickInteractive popup. Assistance may be required. to see the completed graph.
If you are drawing a graph to show only the data in the table, you plot individual points on the graph. If you are drawing a graph to represent the relationship between x and y that is shown by your data, then you connect the points with a line that continues on in either direction.
Write a verbal description and an equation, and draw a graph that each represent the relationship shown in the following data tables: