Using Graphs to Determine the Constant of Proportionality | schizofrenia.info
all about RELATIONSHIPS and how things change. In ALL the constant and change the proportionality sign into an equals sign. Physics graphs to look for. Direct Proportion and The Straight Line Graph. Back Forces Physics Mathematics Contents Index Home. Straight line graphs that go through the origin, like the. A proportional relationship is a special kind of linear relationship, but while A linear function is very easy to graph, because it is a straight line.
The k is your constant of proportionality. The x is the value you multiply your constant by and your y the resulting values. For the toy model example, the x values are the model measurements, the y values are the real-world measurements, and k is A Graph Showing a Proportional Relationship So, what does a proportional relationship look like when it's graphed?
Direct Proportion Graph | Zona Land Education
It looks like a straight line, like this. This particular graph is actually a very useful one you can use in cooking. You can use this graph to help you figure out how to halve your recipes. Say you have a recipe that makes 24 cookies, but you only want to make 12 for a date night. You can find the amount given in the recipe on the x-axis and then find what it converts into on the y-axis. For example, 5 tablespoons convert into 2. You know that this has to be a proportional relationship because your ratios have to be the same for your cookies to turn out the same.
If you add more of one ingredient over another, your cookies won't turn out the same. Finding the Constant of Proportionality Now that you have the graph of your proportional relationship, you can actually use this to help you find what your constant of proportionality is. Because this graph is used to halve your recipe, what do you expect the constant of proportionality to be?
Let's see if that is what you get. So for this first pair, when X is one, Y is one half, so this ratio is one half over one. Well one half over one is just the same thing as one half. 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.
Proportional relationships: graphs
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. 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. 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.
Lawless Teaching : Physics : Proportionality
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.