Lesson video

Hello, and welcome to another video.

In this lesson, we'll be going through linear and nonlinear graphs.

I am Mr. Maseko, make sure that you have a pen, a pencil, a ruler, and something to write on it before moving on with this lesson.

Now, once you have all those things, let's get on with today's lesson.

So first try this activity.

Find some similarities between the characteristics of these graphs.

The two students have already made some observations.

So pause the video here and give this a go.

Okay, let's see what you have come up with.

Well, what similarities can you see? Well, if we look at this, the purple, the green and the red are all straight lines whereas the orange is a curve.

And well, the orange and the green both have parts that tilt upwards, just like the orange and the red both have parts that tilt downwards.

What else? Well, you can see that the orange and the green, all go through the point.

Now there are other relationships that you could have come up with and I look forward to seeing them when you share your work.

So, linear graphs are what? Straight lines.

Linear graphs are straight lines.

So the purple line, the green line and the red line are all linear graphs.

Whereas the orange line is not because it is not a straight line.

And we saw in the previous lesson that we can give names to graphs that are straight lines.

And we can also give names to graphs that are no straight lines.

So graphs that are non-linear.

So pick some coordinates on these graphs and see if you can name them.

So pause the video here and give that a go.

Okay, let's see what you come up with.

Well, I'm going to start with the green line.

But on my green line, you should have seen if you picked three points or any points you wanted, I'm going to pick three, so the point , the point , and the point.

You should have noticed that the Y ordinate is always equal to the X ordinate in there add two.

Now on my red line, again, we're going to pick three points on that red line, so the points , the points , and the points.

And for this one, you should have noticed that the Y ordinate is always equal to four take away that X ordinate.

Now that was a hard relationship to spot.

So really well done if you spotted it.

Now, what about that curve? Well, the only three points we can see properly on that curve, which are , , and.

Did you come up the relationship for this curve? Well, it turns out that the relationship for this curve, the Y ordinate is always the X ordinate squared.

Look at this.

When the X ordinate is negative one, negative one squared, so negative one times negative one gives us positive one.

When the X coordinate is one, one times one gives us one.

When the export is two, two times two gives us four.

So if the X coordinate is three, what would the Y ordinate be? Good, it would be nine.

So on this graph, there's another point, and I'm going to extend this graph further, and there'd be another point here at the.

So that line, our graph is Y equals X squared.

You'll deal more with these types of graphs later on in your maths education.

So let's look at the relationship between linear and non-linear graphs.

And we are going to be focusing on the change in the Y ordinates when the X coordinate increases by one, because that is a sure way to tell if your graph is linear or nonlinear.

Let's see what I mean.

If we look at a linear graph every time the X ordinate increases by one, the Y ordinate increases by one.

It doesn't matter where you are on the graph, every time the X ordinate increases by one, the Y ordinate increases by one.

So no matter where you on the graph, every time the X ordinary increases by one, the Y ordinance increases by one for this particular linear graph.

So we can say, the change and the Y ordinates when X increases by one is constant throughout the graph.

So for all linear lines the change in the Y ordinance when X increases by one is constant throughout the line.

But if you look at non-linear graphs, the change in the white ordinance when X increases by one.

So from here to here one, X increases by one, the Y coordinates increases by one.

But from this point to this point, when X increases by one, the Y ordinates increases by three.

So for a non-linear graph, a change in the Y ordinate when X increases by one is not constant throughout the graph.

So the change in the Y ordinate when X increases by one is not constant through the graph.

And that is one of the main differences you will notice with linear and non-linear graphs.

And we'll talk more about what this change in the Y ordinates when the X coordinate increased by one is actually called in the next lesson.

Video here and give this independent task ago, the grid will help you to do this.

Okay, now that you have gone through this, let's see what you've come up with.

Well, we want to test for three, that would lie on a linear graph.

A linear graph is what a straight line and what we figure out about straight lines? That the change in the Y ordinate is always constant when the X ordinate increases by one.

So let's pick, I'll pick the first point at , then my next point at.

But what's happened? The X ordinate has increased by one and the Y ordinate has increased by three.

So we've got to do the same thing to find our next point.

That X ordinary increases by one, the Y ordinary increases by three, and there is the next point on our line.

And that gives us three coordinates on that line.

We will do the same thing backwards.

If we go down three and back one, we can find another point on this line, and I have given you four coordinates on that linear line.

What are they negative? , We have , we have , and we also have the point.

Upwards there was.

Okay, now let's try this again.

Well, let's do start from negative five, from the point , where can we go? Well, let's say we have a point at.

What would the next point be? Well, we've gone one up on the X and two up on the Y.

So if you do the same thing, one up on X, two up on the Y we end up at the point.

You can do the same thing.

One up on the X two up the Y, we ended up at the.

Now I've given you four coordinates and all I ask you to do was do three for your linear lines.

But the main thing I wanted you to notice was what? That the change in the Y ordinance for a single increase in the X ordinate is constant on a linear graph.

Now, let's look at that second question.

It says, give two coordinates that would lie on a linear graph with and.

Where is ? Our is there.

And ? Our is here.

So what's happened? We've increased X by one, and Y is increased by two.

So if we look at the X ordinate before that, that was three and the Y ordinate has to increase by two.

So if you look at this, yeah.

So the point that lie that line is , another one.

Well, go backwards again and you find the point.

Those two points are on a linear graph with , and.

Now that relationship will forever be important as we go forward in this lessons.

Now for the explore task, find some linear graphs that base points would lie on.

If you want to try this without a clue, go now, whereas if you need a clue, I'll give you one.

So think about naming graphs.

What's a linear graph that has the in it.

Well, you could have Y being equal to X, as a linear graph can you figure it out anymore? Try it now.

Okay, now that you've tried this, let's see what you've come up with.

Well, the that could lie in many linear graphs.

It could be a Y is equal to 2X, Y is equal to 3X, because three times zero gives you zero.

For point , for that could be an Y equals X, add six.

What else? Y equals 3X, you could've done Y equals 2X at three.

What about four negative four? You could have done Y equals X take away eight or Y equals negative X.

If you have been creative, what else? Well, you could have done well, Y equals 2X.

So two times four, that gives you eight, to get from eight to negative four.

Well, you've got to take away what? 12.

So you could have done, Y equals 2X take away 12.

Now that's another creative one you could have had.

So the next one that we're looking at is can you find nonlinear across for this point? Now we didn't touched too much on what the equations of non-linear graphs look like, but you could have done Y equals X squared for these first two points, because you should have noticed that in the non-linear graph you saw earlier today, those two points were on that line.

So, I look forward to seeing what other answers you came up with.

And if you want to share your work, ask your parent or carer to share your work Twitter, tagging @OakNational and #LearnwithOak.

Thank you for participating in today's lesson.

Bye for now.