Chapter Closure
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Rule: - 2x+5=y
| IN (x) | - 10 | 0 | 5 | 1 | 25 | - 6 | 8 | - 1 | 6 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| OUT (y) | 25 | 5 | - 5 | 3 | - 45 | 17 | - 11 | 7 | - 7 | - 15 |
We are asked to find the rule between the values and fill in the missing entries in the table below.
| IN (x) | - 10 | 0 | 5 | 1 | 25 | - 6 | 8 | - 1 | 6 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| OUT (y) | 5 | 3 | - 45 | 17 | - 15 |
We see that the ratio between the differences equals - 2. - 48/24=- 2 This suggests that every input is multiplied by - 2 in the process. Let's check if the inputs multiplied by - 2 gives the outputs from the table. We will consider only on the inputs that we already have the outputs for.
| IN (x) | 0 | 1 | 25 | - 6 | 10 |
|---|---|---|---|---|---|
| - 2x | - 2(0)=0 | - 2(1)=- 2 | - 2(25)=- 50 | - 2(- 6)=12 | - 2(10)=- 20 |
| OUT (y) | 5 | 3 | - 45 | 17 | - 15 |
We can see that in each pair, the input multiplied by - 2 is 5 less than its corresponding output. Let's then also add 5 and see if this is our rule.
| IN (x) | 0 | 1 | 25 | - 6 | 10 |
|---|---|---|---|---|---|
| - 2x+5 | - 2(0)+5=5 | - 2(1)+5=3 | - 2(25)+5=- 45 | - 2(- 6)+5=17 | - 2(10)+5=- 15 |
| OUT (y) | 5 | 3 | - 45 | 17 | - 15 |
We can see that the numbers produced and the outputs match now. This means that multiplying the input value by - 2 and adding 5 gives us the corresponding output. Let's write that algebraically. - 2x+5=y
Now we can fill in the gaps in our table. Let's recall the pattern we found. - 2x+5=y We can use it to calculate the missing outputs. This will allow us to complete our table!
| IN (x) | - 10 | 0 | 5 | 1 | 25 | - 6 | 8 | - 1 | 6 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| OUT (y) | - 2( - 10)+5=25 | 5 | - 2( 5)+5=- 5 | 3 | - 45 | 17 | - 2( 8)+5=- 11 | - 2( - 1)+5=7 | - 2( 6)+5=- 7 | - 15 |