Answer:
Alright you have a situation where someone is going to a movie theater and they're going to spend a bunch of money. So they've got 5. So 5 for every bag of popcorn. Um And then they're also gonna buy some drinks and the drinks are equal to um half of the cost of a bag of popcorn. So half of 5. That means that the drinks are equal to um 30 total equal to 2.50 for every drink. All right so how do we graph this? Well for one we need to decide which variable is going to be our X. Axis and which one's going to be our Y. Axis. Let's choose the P. For popcorn. Um We'll do it vertically. Popcorn um for the Y. Axis and then we'll choose um the X. Axis. For the D. For the drinks drinks. Alright so this is set up very very nicely for us to use the intercept intercept method to find our graph. So the way we do that is we just set each variable equal to zero at different times. To solve for the intercepts. So um if we set the drinks equal to zero and we only bought bags of popcorn would be 30 is equal to five p. And if we set the popcorn equal to zero, we only bought drinks would be 30 is equal to 2.5 times the number of drinks. So in the first situation you would buy a maximum number of six bags of popcorn. And in the other situation you'd buy a maximum number of 12 drinks. Um So let's let's plot this six bags of popcorn. So we'll go up a total of 612 3456. And again this point is 06. And this means like all the money is spent on popcorn. So six bags of popcorn and then the alternate situation be spent all the money on drinks. So go over 12 12345678 9 10, 11, 12. Here's 12 And that's this 0.12 zero. So 12 drinks, no bags of popcorn. So 12 drinks. But the more likely situation is that it's some combination. And the way we show that with our graph is we draw a line Connecting these two points and on this line every single point that's on here um is a possible solution. So the slope of this line is negative 1/2. Which means that um it's hard to buy like a half bag of popcorn. So you really can only kind of go down in single steps but you could buy five bags of popcorn four bags of popcorn, 32 on my line is obviously a little bit off, but each of these are possibilities of what you could buy the same thing in terms of drinks, you're not going to buy half of a drink. Um, They don't really let you do that, but um, assuming that there's only one size, this is all you could do. So, um, here's a graph. I hope that this is helpful and best of luck.
Explanation: