Operations and Algebraic Thinking 222-226
Worked example identifying proportional relationships from graphs.
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- 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?(12 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.(12 votes)
- I attempted to do the assignment, But I couldn't press the check button(4 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.(3 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 ??(2 votes)
- You had the right idea but you didn’t quite say the last part correctly.
Every proportional relationship is a linear equation but not every linear equation is a proportional relationship.(4 votes)
- I didn’t understand :((2 votes)
- What didn't you understand? If you explain yourself more fully, people can help you better!(4 votes)
- what is a slope(3 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.(1 vote)
- the only way it can be proportional is where it has to go through the origin(2 votes)
- for the first question there are 0 correct proportional relation ships because none of them have a strait line.(2 votes)
- [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.