Main content

## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 3

Lesson 13: Constructing linear models for real-world relationships# Linear functions word problem: pool

CCSS.Math: , ,

Sal is given a verbal description of a real-world relationship involving a pool being filled with water, and is asked to draw the graph that represents this relationship.

## Want to join the conversation?

- why did he plot the second point on (10, 160) and not in (10,60)?(6 votes)
- At1:42in the video, he's already plotted (20, 220) and he's deciding where to put the second point. He's decided that the second point is going to be (10, y), where y is the water level at x = 10 minutes. The information required to reverse engineer this information is in bold print below:
`Omojobi is 220 centimeters tall. He wanted to fill up his pool so that the water level would be as high as he is tall.`

**The water level rose by 6 centimeters each minute**and reached the desired height after 20 minutes.

10 minutes at 6 cm per minute = 10 min โ 6 cm/min = 10โ6 cm = 60 cm

The water level increased by 60 cm**from y cm at 10 minutes**to 220 cm at 20 minutes.`y + 60 cm = 220 cm`

y = 220 cm - 60 cm

y = 160 cm โ second point plotted was (10, 160)

If you incorrectly assume that the water level increased by 60 cm**from 0 cm at 0 minutes**, then you would get the point (10, 60). In fact, the water level was at 100 cm at 0 minutes. You cannot assume an empty pool! Since you were not given the initial value of the water level, you have to work**backwards in time**from the point (20, 220), rather than forwards in time from the (unknown) y-intercept.(19 votes)

- 220 cm is very tall for a person, 7 ft 4 in. Thats really really tall. Even taller than my dad who is 6'9"!(11 votes)
- 2 meters and 20 cm. I noticed that myself! I guess they aren't as good with metric in the USA.(3 votes)

- How do I know whats X and whats Y.(5 votes)
- Find which one is the variable being changed. It is time in this one because time is passing and the water level depends on it.(1 vote)

- dude, what the heck? can someone explain why we didn't just choose a random starting x-coordinate? seriously, its the little things that mess one up.(4 votes)
- You can't draw a specific line by picking random number. If you pick random values, you get a random line.

To graph a specific line, you need either:

1) Two points (x, y) that are on the line

2) One point (x, y) and the slope of the line.

So, when given a word problem like this, you need to read it carefully to figure out what information you are given.

The problem tells you the pool needs to be filled to the same height as Omojobi. This is 220cm. It also tells you that it takes 20 minutes to reach this height. This is one point (20 min, 220 cm).

The problem also tells you tht the pools rose by 6cm per minute. This is the slope.

Sal needs to start graphing using the given point (20, 220). He can then find additional points by using the slope. This is where a little randomness can creap in. Sal chose to go with 10 minutes. He could have picked some other time for his 2nd point. But, for what ever time he picks, he needs to ensure the the Y value will correspond to the slope of the line. At 10 minutes, the time is 10 minutes earlier than 20. So, applu the slope: 6/1*10/10 = 60/10. This tells us the new point needs to be 60 cm smaller and 10 minutes earlier = the point (10, 160).

If Sal had chosen to go 5 minutes earlier (so at time 15 min), then the slope change would be: 6/1 * 5/5 = 30/5. This would create a point of (15, 190).

Hope this helps.(2 votes)

- I don't understand this

My brain cells are about to fry up someone help me ๐ญ๐ญ(4 votes) - I know how to find my slope when I'm just given (Y*-Y*)\X*-X*).But I get so confused with word problems.(3 votes)
- Either find 2 points or find on point and the slope.(3 votes)

- Does it make any difference if I put the second dot directly on 100 centimeters(y axis) when Sal put it on above 10 sec where 160?(2 votes)
- That would be ok. (0, 100) is a point on the line. And, you can graph the line using any 2 points on the line.(4 votes)

- The y-intercept changes if you take any other point along the x-axis; so, how did Sal know the water level at the beginning was exactly 100 cm when it could have just as easily been at an another height? It all seems arbitrary to me.(2 votes)
- The y-intercept is the point where the line crosses the y-axis. This is a fixed value for any given line since every point on the y-axis has an x-coordinate of 0.(3 votes)

- Why was 10 mins chosen? I'm not sure where the 10 came from as opposed to another number such as 15.(1 vote)
- Remember, lines have an infinite set of points (x, y).

I think Sal chose the 10 because the math was easy.

The problem tells us that after 20 mins, the water is at 220 cm. That's one point (20, 220).

Sal found his 2nd point by using the slope. The water rose 6 cm each min. So, in 10 minutes the water rose 6(10) = 60 cm. Sal subtracted 10 from 20 = 10 and then subtracted 60 from 220 = 160 to get his 2nd point (10, 160).

Hope this helps.(3 votes)

- I'm so confused om this right now(1 vote)

## Video transcript

- Omojobi is 220 centimeters tall. He wanted to fill up his pool so that the water level would be as high as he is tall. So that the water level, I guess, would be 220 centimeters tall. The water level rose by
six centimeters each minute and reached the desired height after 20 minutes. Graph the pool's water
level, in centimeters, as a function of time, in minutes. Well, they do tell us
one interesting thing. They say that the water level reached the desired
height after 20 minutes. And we know what the desired height is, the desired height is to be as tall as, or to be as deep as he is tall, or as high as he is tall. And that is 220 centimeters tall. So they're telling us essentially that the water level of the pool after 20 minutes is 220 centimeters, so we can plot that. So after 20 minutes, so we can plot that point right there. After 20 minutes, we
are at 220 centimeters. So we would be right there. Now the other question is where would we put this point? We need another data point
in order to define a line. And so they tell us that the water, you might be tempted to say, "Okay, maybe the water level was "at zero to begin with," but
they didn't tell us that. Maybe when he started filling the pool there was already some water in there. So we have to be a
little bit more careful. But they do give us some information. The water level rose by six
centimeters each minute, it rose by six centimeters each minute. So at 20 minutes, we know we're at 220. And if we rose six
centimeters each minute, where would we have been, let's say 10 minutes ago? So, where would we have been at time 10? So, every 10 minutes, if the water level is rising six centimeters a minute, it would be rising 60
centimeters every 10 minutes. So 10 minutes ago, we would
be 60 centimeters less. So 60 centimeters less than 220. That's 20 centimeters less, that's 40 centimeters less, that's 60 centimeters less. So, if you go back in time 10 minutes, you would be 60 centimeters shallower, or less high, and 220 minus 60 is 160. Now, I think I'm done. I
think this describes it. Now let's see if it makes sense. This is telling us that at time zero there was, before he started filling it, there was already 100
centimeters in his pool. And then after 20 minutes, he's done. And is that consistent with
six centimeters a minute? Well, based on this,
it took him 20 minutes to get to 220, but that's
an incremental 120. To go from 100 to 220
is 120 more centimeters. So in 20 minutes, he got 120 centimeters. Well 120 centimeters divided by 20 minutes is six centimeters per minute. So this is looking good
and we got it right.