Kid2Kid Video Transcript
Algebra I: Module 1 Lesson 2 – Writing Equations to Describe Functional Relationships (table ->
equation)
What’s up everyone? This is Rochelle from the Algebra I Tutoring Club. Today, we are going to take a
look at how to write an equation given a table. These two questions that we are going to look at were
submitted by Chloe from Dallas, Texas. So, let’s start with problem number one.
Problem 1 says, “Which problem best represents this relationship?” You’re given a table. Independent
Quantity: 0, 1, 2, 3, 4. Dependent Quanity – you’re given the numbers -3, -1, 1, 3, and 5. So here’s the
first thing you have to know, independent usually is the x-variable. Think of it like…I’m independent;
I’m going to x you out of my life. Dependent is usually the y-variable in Algebra….”y” are you so
dependent on me? If you think of it like that, it’s easier for you to have.
Now, let’s get down to the question. If you don’t know what the word function means, know that
function is another word for equation. So if I had to read it again, it would say – which equation best
represents this relationship? Ok, let’s take a look at the answer choices. This is so easy, so easy. This
notation here, what our teachers call notation f(x), this actually stands for y, which is your dependent
variable. You’re given the x in each one of your answers. All you have to do is substitute or replace all
of your x-values into each one of your equations and see what the answer is. It’s real simple.
So let’s start with A. A says y = 6x. My first value for x is zero. You know that when you have a
number next to a letter, it means multiplication. So you have six times zero, which we know is equal to
zero. According to your table, your answer should be - 3. So I know that A cannot be my answer
because my numbers don’t match.
My second equation is y = x - 3. I’m going to go back to my original value, zero, so this would be equal
to zero subtract three. Don’t get confused, zero subtract three is not three. It’s negative 3. What do
we want for an answer? We want negative 3. So I have my answer, right? No, you don’t have your
answer. You have to check all of your values until you get all of them correct.
So let’s try the value for 1 using the same equation y = x-3. Then we will do one minus three. One
subtract three is negative two. According to my table, I should get negative one, so I know that this
cannot be my answer.
Alright, let’s try C. C says y = 3-x. I’m going to start with zero again, so this is three subtract zero which
is equal to three, not zero. And according to my table, I should get negative three. You with me? Ok, C
can’t be my answer. So out of a process of elimination, you know the answer has to be D, but try it just
in case. Ok, let’s do D. So this will be y = 2x-3. Starting with zero, you have two times zero minus
three. Two times zero is zero. Zero subtract three is negative three. I have that for my first value.
Ok, let’s do 1. So you have y=2x-3. Two times one, subtract three. Two times one is two. Two
subtract three is negative 1. Check!
Kid2Kid Video Transcript
Chloe, I hope this helps you out. This question has been submitted about five times, so I’m going to do
this question, plus the one that she submitted after that. Let’s take a look at it.
This problem says, “The table shows values for the independent and dependent quantities in a
functional relationship. Write the function that describes the data in the table.” Ok. This one is
probably a little bit harder, simply because they don’t give you the equations but that doesn’t mean that
you can’t do it. Let’s go back to what we did in the first problem.
We know Independent stands for x. Dependent stands for y. The first thing you want to do is to find
out the number that comes in front of the x. Here’s how you do it, you have to stay with me. You have
to find the difference in each one of your independent values. So going from one to two, your change is
one. How did I get that? I’m subtracting. Two subtract one would give me one. Ok, let’s’ do the next
one. Five subtract two would give me three. Let’s do the next one. Six subtract five would give me
one. And eight subtract six is two. Not hard, right?
We still have a lot of numbers and we still have some things to do, so I’m going to walk over to the
dependent side and do the exact same thing. Let’s find the difference between these particular values:
Seven subtract four is three. Sixteen subtract seven is nine. Nineteen subtract sixteen is three.
Twenty-five subtract nineteen would be six. My next thing is now that I have my values for my x and
my y, here’s what we’re going to do. We’re going to divide both of these numbers. Three divided by
one; that will give me three. Nine divided by three; that’s also going to give me three. Three divided
by one; that’s going to give me three. Six divided by two will also give me three. What does this tell
me? This tells me that every time I’m going to change, it’s going to increase by three. So here’s what
you’re going to do. You’re going to go back to the other side.
I know that the number in front of the x has to be a three. So far, I have y = 3x. Is that my answer?
Check it out and see. Ok, how do you check it out? Do what you did in the first problem. If I put a one
where the x is, three times one will give me three. What should I get? I should get four, so I know that
this couldn’t be my answer. Let’s try the second one with the same problem, y = 3x. This time, I’m
going to plug in two. So I have three times two which is six but I know my answer should be 7.
Here’s what you do, it’s like playing a guessing game. Figure out what you need to add or subtract to
your equation to get your answer. It’s that simple. I’m going to go back to the first one. I got my
answer three when I plugged in the one. What do I need to get to four? I need to add one to three.
What about the second one? If I plug in 2, 3 x 2 is 6 so what do I need to get a 7. I need to add a 1. So
if I go back, what can my equation be? Maybe it’s y – 3x +1.
Let’s try that but I’m going to try for a different value. Let’s try for 5. Three times five plus one. Three
times five is equal to fifteen. Fifteen plus one gives me 16. To recap, what do you do? Find a change in
your x by subtracting. Find a change in your y by subtracting. Divide those two numbers to find your
constant change. That’s the number that goes in front of your x. Once you do that, try your values out
Kid2Kid Video Transcript
to see if that’s your right answer. If not, try the guessing game to add and subtract to find your right
answer. I hope that helps you out.