Exercise 118 Page 143

We are asked to find the rule between the values and fill in the missing entries in the table below.

Rule

Let's start with the rule. We can focus on two inputs, 1 and 25, because we know their outputs. What we need to do is to evaluate the differences between the inputs and between their corresponding outputs, 3 and - 45. Difference of Inputs:& 25-1=24 Difference of Outputs:& - 45-3=- 48We 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.

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.

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

Completing the Table

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!