Question

A teacher has a 2-gallon (32-cup) container of juice. She gives each student One-half cup of juice. Which equation represents the amount of juice that remains, y, after x students are served?

Answer 1

Answer choices?

Answer 2

you don't need answer choices most of the time, if ever really, to be able to help answer a math question smh

like how does having the answer choices help you in guiding them to the answer?
"OooOOOoO do you see answer choice B?!? those numbers are so pretty that it has to be the answer"
that's not how it works lol

You work it out, you get the answer, and you check with the answer choices and what you got should be listed and you go with that

ez pz

however, yes answer choices are beneficial in seeing if they're using cups or gallons as the units, but it most likely has to be cups. And regardless, if it turns out to be gallons, it's not hard to do it once you understand the concept

Answer 3

In this question, we are asked to write an equation

Here is the slope-intercept form for an equation

y = mx + b

m is our slope. This is an amount that we are constantly increasing or decreasing by. (This number will either be positive or negative depending on whether we are constantly increasing or constantly decreasing)
b is our y-intercept. This is the constant amount we are starting off with

now I'll do an example for you and you can see the similarities to your own question and you can then try to solve your own question and don't worry! I'll still be here if you get stuck

Example:
Charlie has 53 toy cars. He goes to school, he gives two of his toy cars to a new friend. Which equation represents the number of cars that remain, y, after
befriending x students?

So he starts off with 53 cars.
Every time he makes a new friend 'x', he gives them 2 cars

What is the constant number that we're decreasing by?
It's 2!
We are constantly decreasing by 2.
When he makes one friend, he gives away 2 cars. When makes another friend, he gives another 2 cars.
So he's constantly giving away 2 cars

Now what's the constant number that he started off with?
53!

So what is our slope?
2!
But hold on a second, is Charlie getting two new cars every time he meets someone? Nope! He's losing two cars. His total number of cars keeps decreasing. That means the slope is actually -2.
Because we're constantly decreasing.

What is our y-intercept?
53!

What is our equation?

Now here we have to be careful
You CANNOT just do
y = 2x + 53
Because if you look at this, this means that for every new friend he makes, he's ADDING two cars
But we know that's not right because he's giving away two cars so that means

The slope isn't actually 2. What did we say it was? It's actually -2! Because we're constantly decreasing.
If he was the one getting 2 new cars from every friend, then it would be +2. But since he's giving it away, he's decreasing by -2 every time so the slope has to be -2

I was just reiterating the point that the slope is not 2 but rather-2

So anyways we have the equation in the form of

y = mx + b
m is our slope which equals to -2
y is our y-intercept which equals to 53

plug it in

y = -2x + 53

Answer 4

Now similarly, can you do that for your own question? It's not very difficult, they've given you the two numbers! You just have to make sure you get whether the slope is positive or negative right and plug it in!!
Also sometimes the y-intercept can also be negative, like imagine if you owed a lot of money so you're in debt. That means you're starting with a negative amount but if you continuously get money

Now try to solve your question!
I'm right here if you get stuck

A teacher has a 2-gallon (32-cup) container of juice. She gives each student One-half cup of juice. Which equation represents the amount of juice that remains, y, after x students are served?