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## Algebra I (2018 edition)

### Course: Algebra I (2018 edition) > Unit 7

Lesson 3: Constructing linear models for real-world relationships# Linear functions word problem: fuel

Sal is given a verbal description of a real-world relationship involving a truck's fuel consumption, and is asked to draw the graph that represents this relationship.

## Want to join the conversation?

- What will be my x intercept and y intercept if the question says that the line passes through the points (-3,7) and (5,-1)?(10 votes)
- Find the slope of the line using the formula
*m=(y2-y1)/(x2-x1)*. Find the equation of the line with the formula*y-y1=m(x-x1)*.**To find the x-intercept**, put 0 in place of y in the equation and solve it.**To find the y-intercept**, put 0 in place of x in the equation and solve it.

So in your case,*m=(-1-7)/(5+3) = -8/8 = -1*

Equation:*y-7 = -x-3*

=>*x+y-4=0*

=>*x=***4**, y=**4**

Hope this helped(13 votes)

- What are Linear functions?(4 votes)
- A linear function is when, in its simplest form, there are no variables with exponents greater than 1. A linear function will result in a straight line on a graph that has a slope and a y-intercept. It can be defined by y = ax + b where a is the slope and b is the y-intercept. I hope this helped you.(22 votes)

- This is like my 4th time watching this. I have no idea what we're doing. This is why I hate home-school because nobody is here to help me in real life. I'm getting so frustrated to the point where I want to cry. Whenever someone tries to explain it to me I have trouble reading what they're telling me and all of the words get mixed around to the point where I give up reading. I don't want to do this anymore. Everyone seems to think it's so easy.(11 votes)
- It can be difficult, but there are people here to help. Can you tell us a little more about where you are getting stuck with the video?(1 vote)

- i am confused i dont get y(11 votes)
- Enrique is driving to Texas. he travels at 70 kilometers per hour for 2 hours, and 63 kilometers per hour for 5 hours. over the 7 hour time period what was Enrique's average speed?

can someone please explain to me this problem.(5 votes)- you need to add 70+70+63+63+63+63+63, then divide it by 7, because you have to get the total number of km traveled, then divide it by the hours.(9 votes)

- I don't understand anything about this! Can someone help?(7 votes)
- totallynotabot

a few seconds ago

Posted a few seconds ago. Direct link to totallynotabot's post “Karl has a truck that he ...”

Karl has a truck that he filled up with 400 LITERS

He needs to drive somewhere far away because [insert reason here]

His truck can consume 0.8 LITERS every kilometer (So every kilometer Karl drives, he consumes 0.8 LITERS of fuel)

We need to graph a line that represents Karl driving. Assuming he drives the same speed the entire way and consumes the same amount of fuel the whole time.

We need at least 2 different points to graph the line

Let's make the AMOUNT OF FUEL the y-axis and the NUMBER OF KM DRIVEN the x-axis

We already know one point, the y-intersect, or when x = 0, which is the starting amount of fuel that Karl has

This point is (0, 400)

Then we need to find out the second point. So, Sal makes a table at2:30and you can follow that as an example.

Distance (km) | Fuel (Liters)*__________________________*

0 | 400 Liters

100 | 400 Liters - 0.8Liters/km*100km

= 400 Liters - 80 Liters

= 320 Liters

Now we know another point on the graph, (100, 320)

You can choose to do any x value or y-value but one thing remains the same; the point is on the line

Hope this helps cuz MAN my fingers are tired(3 votes)

- For the fuel and kilometer question in the example can we write the question in y-intercept form like this Y=400-0.8x(5 votes)
- Yes you can, if y is the liters of fuel and x is the kilometers driven. Nice math!(4 votes)

- It is so confusing(4 votes)
- I have to say this kind of linear functions just like prediction , even though something not really happen but you can calculate the result like how far can a car drive consumes all the fuel in tank.

Every value in the domain has a corresponding value in range , people just find out the relationship between them and use the algorithm and variables to describe this relationship, but sometimes data actually is not so "consecutive", instead, it's kind of discreate(4 votes)- But even with your example of cars and gas, while it is continuous, in real life, you would not say how far can you drive with 8.34349683 gallons of gas, while you could calculate, but it has no practical purpose. So probably the smallest increment that would be used is tenths of a gallon which would create a discrete graph.(0 votes)

- So the equation for this problem would be

y=400-0.8x ?(2 votes)- Yes, that would be the equation for the problem in the video.(3 votes)

## Video transcript

- [Voiceover] Karl filled
up the tank of his truck with 400 liters of fuel
and set out to deliver a shipment of bananas to Alaska. The truck consumed 0.8 liters of fuel or eight-tenths of a liter of fuel for each kilometer driven. Graph the amount of fuel
remaining in the truck's tank in liters as a function of distance driven in kilometers. And right over here we
have, we have a graph where we have a coordinate plane where our horizontal coordinate
is distance in kilometers, and our vertical, our vertical
axis is fuel in liters. So we can define the line by
moving these two points around, because two points define a line. And so, let's just think about two points that we could figure out. Can we figure out the fuel
at two different distances, and then that will help
us define the line. Well, the first thing that
we might want to think about is, well, what about before
we've traveled at all? That might be the easy
thing to figure out. What was the amount of fuel in the tank when we haven't traveled at all? And they tell us that in this passage. And I encourage you to pause
the video and think about that. Well, they tell us Karl filled
up the tank of his truck with 400 liters of fuel
and then set out to deliver a shipment of bananas. So before he had driven at all, right after he'd filled his tank, he had 400 liters of fuel. So we could say when
distance was zero kilometers, he had 400 liters of fuel. So we have one point on that line. Now we gotta think about
where we might want to put, where we want to put this other point. And the way I think about it is, well, let's just, we know he's consuming, he's consuming eight-tenths
of a liter of fuel for each kilometer driven. But they don't have, you
know, we're not going by one kilometer, two kilometers. They're going by, this is like 50 kilometers, 100 kilometers. So let's think about how much fuel he would have consumed after
driving 100 kilometers, and if he consumed that
much, we would subtract that from the amount of fuel he started with, and then that would tell us, that would tell us where
this point would be. It's going to be some place over here, and it's going to be, it's
going to be below 400, 'cause we're consuming fuel. Fuel should be going down
as distance increases. This should be a downward-sloping line. So I have my, I have my scratchpad here. Let me, let me get it out. And I have the same question there. It just gives us all the same information. But what I want to figure
out is, so we already know, we already know that. So we have distance, distance. Let me, I'll just write. Actually, let me just
write the whole thing. Give myself a little bit more space. Distance in kilometers.
Distance in kilometers. And then you have fuel, you have fuel in liters. You have fuel in liters. And we already figured out that before he got on, right
after he filled up his tank but before he set out on his trip, at distance zero kilometers
he had 400 liters of fuel. And we've already actually plotted that. But then we said, well what
happens at a hundred kilometers? At a hundred kilometers,
how much fuel will he have? Well, they tell us that he
consumes 0.8 liters of fuel for each kilometer. So, 0.8 liters per kilometer, and then
we just multiply that times the number of kilometers. So, times 100 kilometers. The units work out, kilometers
divided by kilometers. We're just going to be left with liters, and then we multiply the numbers. Eight-tenths of a hundred, well that's going to be equal to 80, and the units are liters, 80 liters. So at a distance of a hundred kilometers, he's going to have consumed, right, let me be careful here. He's going to have consumed 80 liters. He's going to have consumed 80 liters. So the fuel, the fuel
is actually going to be what he started with, what he started with minus how much he consumed. So it's going to be minus 0.8, and if we want to write the units there. I might as well, so,
you know, this is liters right over here. This is 400 liters. And I can write this
kilometers, kilometers. It's going to be 400 liters minus 0.8 liters per kilometer times, times, let me make that clear, times 100, times 100 kilometers. And same thing, kilometers
divided by kilometers, and we are left with 400 liters
minus 0.8 liters times 100. Well, that's just going
to be equal to 400 liters, which is how much he started with, minus eight-tenths of a hundred is 80, and the units left is 80 liters. So 400 liters minus 80 liters, that's going to be 320 liters. So when he has traveled
a hundred kilometers, he will have 320 liters left in his tank. So let's plot that. So when he has traveled
a hundred kilometers, actually, I just randomly
had put the point there, he is going to have 320
liters left in his tank. And just like that, we have
plotted the line that showed how much fuel he has in his tank as a function of, as a
function of distance traveled. And you can even see from this that he's going to run out of fuel at the 500-kilometer mark.