# Physics proportionality relationship and graphs

### Proportional relationships: graphs (video) | Khan Academy

Direct Proportion and The Straight Line Graph. Back Forces Physics Mathematics Contents Index Home. Straight line graphs that go through the origin, like the. Because the constant of proportionality only exists for linear relationships, you can use the graph of a proportional relationship to figure out. As you can see from our blog Equations in GCSE Physics, there are a lot of The proportionality relation between acceleration and resultant force (a A graph of two variables which are directly proportional to one another.

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.

**Linearizing Graphs in Physics**

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.

### Curve Fitting – The Physics Hypertextbook

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.

- Direct Proportion and The Straight Line Graph
- Curve Fitting

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. This right over here is the graph of Y equals X squared. So this one also is not proportional. So once again, these three points could be sampled from Y equals one half X, these three points could be sampled from, let's see, Y is equal to, let's see, it looks like a line when So it's a linear relationship, but it does not go through the origin, so it's not proportional.

And these three points look like they could be sampled from Y equals X squared, which goes through the origin. When X is zero, Y is zero, but it's not a linear relationship. If one quantity increases by a certain factor, the other quantity decreases by that same factor.

## Proportional relationships: graphs

We use the same symbol as for proportionality, but represent one quantity by its inverse, so: Proportion Equations All proportional relationships can be rewritten in the form of an equation with a constant of proportionality.

So our proportional relationship can be rewritten from: If we look at our previous two examples: We will use this fact in several parts of the course. Other Proportional Relationships Proportional relationships can get more complicated than simply directly or inversely proportional.

Very often quantities depend on the square root or cube of another quantity. One relationship we will see a number of times on the course is called inverse square proportionality. For example we will later see that the force between two masses due to gravity is inversely proportional to the square of the distance between the masses, or: Detecting Proportionality As explained in the introduction, physics and science in general are concerned not just with theory, but practice as well.

As part of this course, you need to be able to recognise when relationships are proportional, particularly as a result of your experiments. You do this by drawing a graph of the relationship.

The following graphs illustrate various types of proportionality: Proportional relationships show a straight line through the origin.