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### Course: Operations and Algebraic Thinking 222-226 > Unit 1

Lesson 5: Graphs of proportional relationships# Identifying proportional relationships from graphs

Worked example identifying proportional relationships from graphs.

## Want to join the conversation?

- So just to make things clear for myself, it has to go through the origin because no multiplication expression has a product of 0 except if at least one of the factors is 0, so if you start at (2,0) there is not a constant factor (you need a constant factor for proportionality) you can use to end in (3,2) am I right?(27 votes)
- Yep, you got it! An easier way to explain it is that if you buy nothing in a proportionally priced store, you will spend nothing.(38 votes)

- I didn’t understand :((12 votes)
- What didn't you understand? If you explain yourself more fully, people can help you better!(6 votes)

- I attempted to do the assignment, But I couldn't press the check button(8 votes)
- I would recommend pressing the “Report a bug” button. It will show up near the bottom right corner of the work page and you can just tell them that it didn’t work.(9 votes)

- what is the difference between a proportional relationship and a linear equation

I noticed that a proportional relationship needs to go through the origin and the linear equation does not have to go through the origin

can we say that that every proportional relationship is a linear equation but not every proportional relationship is a linear equation ??(5 votes)- You had the right idea but you didn’t quite say the last part correctly.

Corrected version:

Every proportional relationship is a linear equation but not every**linear equation**is a**proportional relationship**.(9 votes)

- ima fith grader i don't understand(5 votes)
- This is 8th grade math

Please go work on something your level(7 votes)

- my brain isn't braining(5 votes)
- My ideas aren't ideaing anymore(6 votes)

- for the first question there are 0 correct proportional relation ships because none of them have a strait line.(4 votes)
- what is a slope(4 votes)
- The steepness of the 'curve/line'. In other words: the difference of the y-value between two points over the change in the x-value.(3 votes)

- the only way it can be proportional is where it has to go through the origin(3 votes)
- Yes, you are correct.(3 votes)

- How would you find the relationship of a line that does not pass through the Origin?(y=....., x=....)(3 votes)
- If you start from y=mx+b, you have to either know or find the slope (m) and the y-intercept (b - where the line crosses the y axis). Going through the origin just means that b=0.(3 votes)

## Video transcript

- [Narrator] We are asked
how many proportional relationships are shown in
the coordinate plane below? And we have the choices,
but let's actually look at the coordinate plane below, to think about how many
proportional relationships are depicted here. So pause this video and try
to answer that yourself. So let's do this together. So, if we're thinking about
a proportional relationship, or the graph of a
proportional relationship, there should be two things
that we're looking for. One, it should be a line. It should be a linear relationship between the two variables. Y should be some constant, some proportionality constant, times X. So you immediately would rule
out our green curve, here because this is not a line. You don't have a constant relationship between Y being some
proportionality constant times X. And for the same reason you
would rule out this blue curve. Now what about this purple line? This might be tempting
because it is a line, but it does not go through the origin. When X is two, Y is zero times X. While, when X is four, Y is one times X. And when X is six, Y looks
to be, 1 and 1/3 times X. So you don't have the same
proportionality constant the entire time. So, we have zero proportional
relationships depicted here. So I would pick zero there. Let's do one more example. Natalie is an expert archer. The following table
shows her scores, points, based on the number of targets she hits. All right, targets hit
and then points she gets. Plot the ordered pairs from the table. All right, so the first one is 1, 3. So here I'm doing it on Khan Academy. My horizontal axis is targets hit, and my vertical axis is points. So, one target hit, three points. So this is going to be one target hit, this is going to be three points. Then I have two targets hit, six points. So two targets hit, and I have six points. And then I'm gonna have
five targets hit, 15 points. So then I'm going to
have five targets hit, and that is going to be 15 points. And so this is looking like
a proportional relationship. In every situation my point is equal to three times the targets hit. So my proportionality constant is three. And you can see if you
try to connect these dots with a line, it will be a line. A line can go through all three of these, and it will go through the origin. So are Natalie's points
proportional to the number of targets she hit? Yes, absolutely.