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## Pre-algebra

### Course: Pre-algebra>Unit 14

Lesson 4: 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)?
• 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
• What are Linear functions?
• 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.
• i am confused i dont get y
• 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.
• 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)
• 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 at and 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
• 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.
• 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.
• For the fuel and kilometer question in the example can we write the question in y-intercept form like this Y=400-0.8x
• Yes you can, if y is the liters of fuel and x is the kilometers driven. Nice math!
• The video simplified:
Karl started off with 400 liters of fuel
so we plot that point(0,400).

Then we multiply 0.8 by 100 and get 80.
subtract the 80 from 400 and we get 320.
Then we plot (100,320).