Identify proportional relationships from graphs (practice) | Khan Academy
They graph the three situations and realize that the two proportional relationships form a straight line, but the time and temperature relationship does not. Direct variation describes a simple relationship between two variables. The graph of the proportional relationship equation is a straight line through the origin . Improve your math knowledge with free questions in "Identify proportional relationships by graphing" and thousands of other math skills.
So the point 0, 0 should be on your line. So if this is the point 0, 0, this should be on my line right over there. Now, let's think about what happens as we increase x. So if x goes from 0 to 1, we already know that a change of 1 unit in x corresponds to a change of 0. So if x increases by 1, then y is going to increase by 0. It's not so easy to graph this 1 comma 0. So let's try to get this to be a whole number.
Graphing proportional relationships: unit rate
So then when x increases another 1, y is going to increase by 0. It's going to get to 0. When x increases again by 1, then y is going to increase by 0. It's going to get to 1. If x increases again, y is going to increase by 0. So just to 1. Notice, every time x is increasing by 1, y is increasing by 0. That's exactly what they told us here. Now, if x increases by 1 again to 5, then y is going to increase 0.
And I like this point because this is nice and easy to graph. So we see that the point 0, 0 and the point 5 comma 2 should be on this graph. And I could draw it. And I'm going to do it on the tool in a second as well.2 Minute Math 9-17 7th Grade Identifying Proportional Relationships in Graphs
So it'll look something like this. And notice the slope of this actual graph over here. Notice the slope of this actual graph.
If our change in x is 5. So notice, here our change in x is 5. Our change in x is 5. You see that as well. When you go from 0 to 5, this change in x is 5. Change in x is equal to 5. When X is four, Y is two, this ratio is gonna be two over four, which is the same thing as one half. 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.
Identifying proportional relationships from graphs
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. And it also goes through the origin.
Proportional relationships: graphs (video) | Khan Academy
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. 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. 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.
Graphing proportional relationships: unit rate (video) | Khan Academy
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.