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### Course: Digital SAT Math > Unit 2

Lesson 3: Linear relationship word problems: foundations# Linear function word problems — Basic example

Watch Sal work through a basic Linear functions word problem.

## Want to join the conversation?

- Man I wanna go home.(127 votes)
- At1:40, what if b is zero? (Like we buy the membership but haven't bought any books yet) The yearly membership cost will be reduce?(0 votes)
- Since this is a real world problem, (0-1 = -1) -1 books doesn't make sense. So your statement is invalid.(16 votes)

- Would the equation m = 60 + 7.60b - 7.60 also work?(7 votes)
- Yes that would work too since the books always costs $7.60 each with a membership. You have to buy at least 1 book, though, since the membership fee is always $60, and you would have no reason to get the membership if you weren't going to buy any books. On the SAT, though, you have to go with the answer choices they give you, and the best one in this case is m = 60 + 7.60(b-1).(11 votes)

- At1:04, he meant to say 15.20 but he actually said 14.20(11 votes)
- Its in the caption bubble thing yes you are right(0 votes)

- hey why are the comments so old. didnt the digi SAT begin this year ?(6 votes)
- it did, but the syllabus for math didn't change much so most of the math videos for digital sat are reused from the paper pen version(9 votes)

- What if the student decides not to buy any book? Then we have zero book which will reduce the membership fee i.e(0-1). I don't understand that(6 votes)
- You are completely right! The equation works if the student actually buys one or more books. It is only true when b ≥ 1.(8 votes)

- At0:50, I don't get it isn't a free book by definition a book that you don't buy? They asked for the amount of money a student spend after BUYING b books and yearly membership.(6 votes)
- b books is the total of books that you buy, including the first one. But the first one is free, so you don´t pay it, so it isn't a book that you don't buy it. you have it, you just don´t pay for it(5 votes)

- If Lee pays $72 in advance on his account at the movie store. Every time he rents a movie, $4 is deducted from his account for every movie rented. How can I write a linear function that models the value remaining in his account after renting x movies. Find the value remaining after renting 4 movies.(5 votes)
- If we want to write a linear function that represents this, the first thing to discuss is what you want x and y to be. The question tells us that y should be the account's value, and x should be the number of movies rented. From here, all we do is fill out slope-intercept form (y = mx+b). We're given two numbers: $72 in advance (aka before any movies are bought), and $4 deducted per movie. Since the slope is given in units of y-per-x, it looks like we're going to be using -4 for slope and 72 for y-intercept.

To find the value remaining after renting 4 movies, you could either count backwards from 72 by 4's or set 4 for x and solve for y:

y = -4x + 72

y = -4(4) + 72

y = $56(6 votes)

- bro this is so easy i feel like i can complete this whole lesson in an hr or less(7 votes)
- I do not understand why c is not the right choice. I am confused as to why you need to subtract b-1(3 votes)
- The first book is free, so you substract that book from b, the amount of books you bought.(8 votes)

## Video transcript

- [Instructor] We're told Fara watched two different TV shows last week. TV show A has 11-minute episodes, and TV show B has 43-minute episodes. Together, she spent 196
minutes watching TV shows. Which equation models this relationship, where lowercase a is the
number of TV show A episodes and lowercase b is the number of TV show
B episodes Fara watched? So pause this video and
have a go at it on your own before we work through this together. All right, now, let's do this together. So we know that together,
she spent 196 minutes watching TV shows. So what we wanna do is
total the amount of time she spent watching TV show A, the amount of time she
spent watching TV show B, and then that should be equal to 196. And so, actually, let me just do TV show A in this orange color. How much time did she
spend watching TV show A? Well, we know that each
episode of TV show A is 11 minutes. So it's going to be 11 minutes times the number of episodes. And they said that lowercase a is the number of TV show A episodes. So this right over here, 11a, is how much time she
spent watching TV show A. And what about TV show B? Well, each episode is 43 minutes. So it's going to be 43
minutes per episode. And how many episodes
are there of TV show B? Well, it's lowercase b is the
number of TV show B episodes. So 43 minutes per episode
times lowercase b episodes, that's how much time she
spent watching TV show B. So if you add the amount of
time she watched TV show A to the amount of time she
spent watching TV show B, that will be her total time, and we know that that needs to be equal to 196. And so let's see which
of these choices have it. That's not that one. Let's see, this one is it, exactly what we got. This is different, and this is different. And we're done.