Chapter Closure
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Recall that a point is always written as an ordered pair, where the first coordinate is the x-value and the second coordinate is the corresponding y-value.
Table:
| IN (x) | - 2 | - 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|---|
| OUT (y) | - 9 | - 7 | - 5 | - 3 | - 1 | 1 | 3 | 5 | 7 |
Rule: y=2x-5
We want to create an x→ y table from the points on the provided graph. Then we can write a rule for the pattern in the table. Let's do it!
Let's take a look at the graph.
Now, recall that a point is always written as an ordered pair, where the first coordinate is the x-value and the second coordinate is the corresponding y-value. (- 2_x, - 9_y) Let's use this information to make our table.
| IN (x) | - 2 | - 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|---|
| OUT (y) | - 9 | - 7 | - 5 | - 3 | - 1 | 1 | 3 | 5 | 7 |
We are asked to wirte a rule for our table.
| IN (x) | - 2 | - 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|---|
| OUT (y) | - 9 | - 7 | - 5 | - 3 | - 1 | 1 | 3 | 5 | 7 |
We can see that as the x-value changes by 1, the corresponding y-values change by 2. This suggests that every input value x is multiplied by 2 in the process. Let's check to see if this is our pattern.
| IN (x) | - 2 | - 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|---|
| 2x | 2(- 2)=- 4 | 2(- 1)=- 2 | 2(0)=0 | 2(1)=2 | 2(2)=4 | 2(3)=6 | 2(4)=8 | 2(5)=10 | 2(6)=12 |
| OUT (y) | - 9 | - 7 | - 5 | - 3 | - 1 | 1 | 3 | 5 | 7 |
Multiplying the input by 2 alone is not the complete pattern. However, we can see that the input value multiplied by 2 is always 5 more than the corresponding output value y. Let's try subtracting 5 in our rule and see if this is our pattern.
| IN (x) | - 2 | - 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|---|
| 2x-5 | 2(- 2)-5=- 9 | 2(- 1)-5=- 7 | 2(0)-5=- 5 | 2(1)-5=- 3 | 2(2)-5=- 1 | 2(3)-5=1 | 2(4)-5=3 | 2(5)-5=5 | 2(6)-5=7 |
| OUT (y) | - 9 | - 7 | - 5 | - 3 | - 1 | 1 | 3 | 5 | 7 |
We have found our rule! Let's write it down algebraically. 2x-5=y