Answer:
See below:
Step-by-step explanation:
Hello! My Name is Galaxy and I'll be helping you today :D. I hope you are having a nice day!
So what we can do is first find the different between two input/outputs. To do that we can first compare them, then calculate for them, and create an equation.
Comparison
First, to figure out the problem, we have to look at its I/Os (Input/Output). We can pick the numbers (1,48) and (2,56).
Before we do it, lets find the difference.
When [tex]x[/tex] is 1, [tex]y[/tex] is 48.
When [tex]x[/tex] is 2, [tex]y[/tex] is 56,
After we look at it, we see that for everyone 1 Input we have, 8 gets added to the output.
Calculating
So, we know that the starting number is 48 and it builds up by 8 on that, so then the starting part of the equation would be:
[tex]o=48+...[/tex]
(The Ellipsis over here does not mean that the number is continuing!)
We can expand on that since we know that it adds up by 8 per number we add, but to make that work, we have to subtract 8 from 48 so that once we get one, we will get a viable output.
After we do the modifications, we get a equation that looks good!
[tex]o=40+8i[/tex]
I is for the Input
O is for the Output
Checking our Answer / Final Answer
Before we move on, we have to check if our answer is correct, lets try inputing the numbers into our function and seeing if it works!
[tex]48=40+1(8)\\48=48[/tex]
The first one looks correct!
[tex]56=40+8(2)\\56=56[/tex]
The second one looks correct as well.
[tex]64=20+(8)3\\64=64[/tex]
This is also correct, we have now verified that this is a correct equation and that it indeed works.
Final Answer: [tex]o=40+8i[/tex]
Cheers! Consider Marking as Brainliest if it helped!
