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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 1: Heart of algebra- Solving linear equations and linear inequalities — Basic example
- Solving linear equations and linear inequalities — Harder example
- Interpreting linear functions — Basic example
- Interpreting linear functions — Harder example
- Linear equation word problems — Basic example
- Linear equation word problems — Harder example
- Linear inequality word problems — Basic example
- Linear inequality word problems — Harder example
- Graphing linear equations — Basic example
- Graphing linear equations — Harder example
- Linear function word problems — Basic example
- Linear function word problems — Harder example
- Systems of linear inequalities word problems — Basic example
- Systems of linear inequalities word problems — Harder example
- Solving systems of linear equations — Basic example
- Solving systems of linear equations — Harder example
- Systems of linear equations word problems — Basic example
- Systems of linear equations word problems — Harder example

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# Interpreting linear functions — Harder example

Watch Sal work through a harder Interpreting linear functions problem.

## Want to join the conversation?

- couldn't khan cut the mistake in2:56through3:26.(0 votes)
- I almost find it comforting that a teacher might also make a mistake; as long as he corrects it in the end!(290 votes)

- At0:31, how do we know what "15" stands for? This video had me confused. Why do we try to find the mystery unit? Do we treat "32" as we would the variable "x"?(26 votes)
- It's because the equation is Gallons = 15 - miles/32. If the miles equal zero, it means the tank is full. So the equation would be Gallons = 15 - 0/32. Gallons = 15 - 0. Therefore, a full tank of gas holds 15 gallons.(36 votes)

- The whole miles per gallon thingy is a bit confusing......... Can anybody explain further to me.....thanks(23 votes)
- Miles per gallon means a total number of miles you can travel using a certain amount of gallons of fuel. For example if your miles per gallon 5, that means, with 1 gallon of gas, you go 5 miles. So 5 miles per 1 gallon.

If your miles per gallon 20, that means, with 1 gallon of gas, you go 20 miles.

So 20 miles per 1 gallon.

Hope this helps.(40 votes)

- why isn't it the 3rd one? It makes more sense. PLEASE HELP(0 votes)
- hi i am aware that the 3 rd option is very confusing. Let me explain. So basically a tank of gas may have the same units which are gallons but be careful here because when they mention a tank of gas, they always are talking about the value 15 gallons as default. Hence if you pick the third one , you will basically be saying that solution is( miles/15 gallons). Hope this helps(10 votes)

- i'm guaranteed to fail my upcoming SAT(7 votes)
- Don't be pessimistic. Just do your best, and let the outcome be the outcome. But make sure to do your best. Otherwise, you will most likely have regrets.

Just don't give up, and remember the SAT does not determine how you live the rest of your life.(9 votes)

- at1:23why did he take the reciprocal of both sides?(4 votes)
- In order to isolate the "units", he must switch out the co-existing variable on the left side.(10 votes)

- In the question about the gas tank (Interpreting linear functions - Harder example), don't we have to say "Alice's car can travel 32 miles per gallon" instead of "to the gallon"? I'm not a fluent English speaker, but I don't recall hearing such a way to say it.(7 votes)
- Honestly, I've grown up hearing it both ways. They're practically interchangeable- it just depends on where you live. You don't have to say it ("per gallon" might make more sense for some people), but in the end, it's the same.(4 votes)

- Can someone please explain to me why it is that he multiplied by miles SPECIFICALLY?(5 votes)
- Because he wanted to cut out the miles from the denominator.(6 votes)

- I am confused when solving the practice questions, because the explanations to the answers are different than the videos provided. The practice questions solve by using a slope? Im lost.(7 votes)

## Video transcript

- [Instructor] Alice fills
up the gas tank of her car before going for a long drive. The equation below, this should be above, the equation above
models the amount of gas, g, in gallons, in Alice's car when she has driven m miles. What is the meaning of 32 in the equation? Alright, let's look up here. This is the gallons that
she has left in her car, and what's going on here? So it makes sense that,
look, when m is zero, when she's driven nothing, she's going to have 15 gallons in her car. And then as you drive more and more, you're going to subtract more
and more gallons from her car. So, this is, this term right over here, this is the number of gallons, this is the number of gallons used up. So why are you dividing, if you have m miles divided by 32, how do you get gallons? What are the units on the 32 need to be? And so let's just think about this. If I have miles, so this is miles up here, and I'm gonna be dividing
them by some mystery units, some mystery units, I need to get gallons. I need to get gallons because
this is gonna be the number of gallons used up. So what are the mystery units going to be? Well, we can treat these units the way we would treat
algebraic variables. So we could solve for units here. So, we could take the
reciprocal of both sides, and we could say the
units, the mystery units, divided by miles, is going
to be one over gallons. Or I guess you say per gallon, it's gonna be one over gallons, and then multiple both sides times miles, multiply both sides times miles, you're going to get the mystery units. The mystery units are going to be, if you multiply both sides by miles. I don't wanna get confused
with this over here. So we multiply both sides by miles, both sides by miles, your mystery units are going to be miles, miles per gallon. So, this right over here,
the units over here, in order for this thing
to come out to miles, in order to come up to gallons, the numerator, you have m miles divided by 32 miles per gallon, miles per gallon. This is telling you how much
mileage you get per gallon for her car, how much she is getting. So, let's look at the choices. Alice uses 32 gallons of gas per mile. Now we have to be very careful. It's miles per gallon, not gas per mile. Alice's tank can hold 32 gallons of gas. No, Alice's tank can
hold 15 gallons of gas. She fills up her tank, and
before she's driven anything, we see here, when m is zero, she's gonna have 15 gallons in her car. So, that's not right. Alice can drive 32 miles on a tank of gas. That's right. The units here are 32 miles per gallon. So, that's that one. Alice's car can drive
32 miles to the gallon. Oh, that was a close one. This isn't 32 miles per gallon, this is 32 miles on a tank of gas. This would be 32 miles over 15 gallons. No, that's not right. That was a close one. Alice's car can drive 32 miles per gallon. That's right. 32 miles per gallon. And if this unit business that I just did, you find it confusing, one
other way to think about it, I mean you could've ruled
out something like this 'cause when you look at this, you could see that
okay, her tank holds 32, her tank holds 15 gallons, is you could have tried this one and you would have seen that
the units didn't work out. If you have 15 gallons, 15 gallons minus m miles divided by 32 gallons per mile, 32 gallons per mile, what will the units end up being here? Especially right over here, you would have miles
divided by gallons per mile, this is going to be minus m times, I guess let me write it this way, m over 32 miles times miles per gallon. Miles per gallon. You get miles squared per gallon, you get all these, you get
these crazy units up here. So hopefully it makes sense that we would pick this last choice, and this one almost got me
when they said tank of gas. I was thinking, my brain
was thinking gallon, I was so already
programmed for the answer. But anyway, yes, this is the last, the last choice is what
we want to go with.