Proportional relationships | LearnZillion
A proportional relationship exists between two values x and y when they can be expressed in the general form y = kx, where k is the constant of proportionality. In this lesson, you will learn how to write an equation that represents the proportional relationship between the total cost and the number of items by finding the. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table Analyze a table to find proportional relationships.
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. But then all of sudden the ratio is different right over here.
Proportional relationships: graphs
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. So this right over here-- This is not proportional. So the key in identifying a proportional relationship is look at the different values that the variables take on when one variable is one value, and then what is the other variable become?
And then take the ratio between them. Here we took the ratio y to x, and you see y to x, or y divided by x-- the ratio of y to x is always going to be the same here so this is proportional. And you could actually gone the other way.
You could have said, well what's the ratio of x to y? When X is negative two and Y is negative one, this ratio is negative one over negative two, which is the same thing as one half. So for at least these three points that we've sampled from this relationship, it looks like the ratio between Y and X is always one half. In this case K would be one half, we could write Y over X is always equal to one half. Or at least for these three points that we've sampled, and we'll say, well, maybe it's always the case, for this relationship between X and Y, or if you wanted to write it another way, you could write that Y is equal to one half X.
Now let's graph this thing. Well, when X is one, Y is one half. When X is four, Y is two. When X is negative two, Y is negative one.
I didn't put the marker for negative one, it would be right about there. And so if we say these three points are sampled on the entire relationship, and the entire relationship is Y is equal to one half X, well the line that represents, or the set of all points that would represent the possible X-Y pairs, it would be a line.
It would be a line that goes through the origin. Because look, if X is zero, one half times zero is going to be equal to Y. And so let's think about some of the key characteristics. One, it is a line. This is a line here. It is a linear relationship.
Proportional relationships: graphs (video) | Khan Academy
And it also goes through the origin. And it makes sense that it goes through an origin. Because in a proportional relationship, actually when you look over here, zero over zero, that's indeterminate form, and then that gets a little bit strange, but when you look at this right over here, well if X is zero and you multiply it by some constant, Y is going to need to be zero as well.
So for any proportional relationship, if you're including when X equals zero, then Y would need to be equal to zero as well.
And so if you were to plot its graph, it would be a line that goes through the origin.
Introduction to proportional relationships (video) | Khan Academy
And so this is a proportional relationship and its graph is represented by a line that goes through the origin. Now let's look at this one over here, this one in blue. 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. Five over two, well five over two is not the same thing as three. It is a so six times 25 hundredths would be a hundredths which is the same thing as 1.
So this one works. What about three and 0.
Grade 7 » Ratios & Proportional Relationships
So three and 0. Am I multiplying by 0. Yeah, if I multiply three times 25 hundredths, I get 75 hundredths so that works. So actually the first three choices are our three answers but let's just verify that the next two are not good answers.
So let's see, if I go from 20 to 5. So that doesn't work. And then going from 11 to 3. Or you could say what's one fourth of 11? Well that's going to be less than 3.