Eighth Grade / Distinguishing Between Proportional & Non-Proportional Situations
Nonproportional definition, having due proportion; corresponding. See more. Definition of linear relationship: A relationship of direct proportionality that, when plotted on a graph, traces a straight line. In linear relationships, any given. is called the relationship between the variables. The relationship can be linear, directly proportional, inversely proportional or non-linear. Linear just means that.
So let's think about whether it is proportional. And we could do the same test, by calculating the ratio between Y and X. So it's going to be, let's see, for this first one it's going to be three over one, which is just three. Then it's gonna be five over two.
Proportional relationships: graphs
Five over two, well five over two is not the same thing as three. So already we know that this is not proportional. We don't even have to look at this third point right over here, where if we took the ratio between Y and X, it's negative one over negative one, which would just be one. Let's see, let's graph this just for fun, to see what it looks like. When X is one, Y is three. When X is two, Y is five.
X is two, Y is five. And when X is negative one, Y is negative one. When X is negative one, Y is negative one. And I forgot to put the hash mark right there, it was right around there. And so if we said, okay, let's just give the benefit of the doubt that maybe these are three points from a line, because it looks like I can actually connect them with a line.
Then the line would look something like this. The line would look something like this. So notice, this is linear. This is a line right over here. But it does not go through the origin. So if you're just looking at a relationship visually, linear is good, but it needs to go through the origin as well for it to be proportional relationship.
And you see that right here. This is a linear relationship, or at least these three pairs could be sampled from a linear relationship, but the graph does not go through the origin. And we see here, when we look at the ratio, that it was indeed not proportional. So this is not proportional. Now let's look at this one over here.
Let's look at what we have here. So I'll look at the ratios. So for this first pair, one over one, then we have four over two, well we immediately see that we are not proportional.
And then nine over three, it would be three. So clearly this is not a constant number here. We don't always have the same value here, and so this is also not proportional. But let's graph it just for fun. When X is one, Y is one. When X is two, Y is four. This actually looks like the graph of Y is equal to X squared. When X is three, Y is nine. At least these three points are consistent with it. So one, three, four, five, six, seven, eight, nine. So it's gonna look something And so, if this really is, if these points are sampled from Y equals X squared, then when X is zero, Y would be zero.
So this one actually would go through the origin, but notice, it's not a line. It's not a linear relationship. So you see that y over x is always going to be equal to three, or at least in this table right over here. And so, or at least based on the data points we have just seen. So based on this, it looks like that we have a proportional relationship between y and x. So this one right over here is proportional.
So given that, what's an example of relationships that are not proportional. Well those are fairly easy to construct. So let's say we had-- I'll do it with two different variables. So let's say we have a and b. And let's say when a is one, b is three.
And when a is two, b is six. And when a is 10, b is So here-- you might say look, look when a is one, b is three so the ratio b to a-- you could say b to a-- you could say well when b is three, a is one. Or when a is one, b is three. So three to one.
And that's also the case when b is six, a is two. Or when a is two, b is six. So it's six to two. So these ratios seem to be the same.
Proportional relationships: graphs (video) | Khan Academy
But then all of sudden the ratio is different right over here. This is not equal to 35 over So this is not a proportional relationship. In order to be proportional the ratio between the two variables always has to be the same.