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Hello, and welcome to another video.

In this lesson we'll be talking about equations of lines.

I am Mr. Maseko.

Before you get on this lesson, make sure you have a pen or pencil, and something to write on.

Okay, now that you have those things, let's get on with today's lesson.

Try this activity.

These are three linear graphs.

What information can you say about the triangle? Pause the video here and give this a go.

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

Well, let's complete the statements the students have made.

We have the red line has a Y intercept at.

Or let's look at the red line, this red line, where does that red line have, let's see, lets' go back.

Where does that red line have a Y intercept? Where does that red line have a Y intercept? Good, see it as a Y intercept at the point , okay.

The blue line has a gradient of what? Well, if we pick a point on the blue line or we go up one on the X , we go up two on the Y, which means the gradient is two.

We increase the X coordinate by one, the Y ordinate increases by two.

What else can you say about these lines? Well, can you see the gradient of the red line? Well, on the red line, we'll pick a point or we go up one on the X.

We go up a half on the Y.

So the gradient, remember we refer to the gradient as M, how do we know this? From Y equals MX add C.

So gradient M is equal to 1/2 and that's for the red line.

What about a yellow line, what's the gradient of the yellow line? Well, take a point on the yellow line, let me go up one on the x-axis, let me go down one on the y-axis.

Meaning a gradient at the yellow line is negative one.

Now let's explore what else we can tell about this lines.

Remembering back from last lesson, we talked about y is equals MX plus C.

Can we state the equations of each of these lines? What did we say last time? Well, remember that the equation of a line is written as Y is equal to MX plus C.

Now this isn't the only way you can write them, but this is the mnemonic coded.

This is the general form, and it's the most common way we see the equation of a straight line written.

So this is the general form.

M was the gradient.

Well, we already know, let's look at the red line.

We worked out the gradient already.

The grading was 1/2, so we can say, Y is equal to 1/2 times X as 1/2 of X.

Now what was C see again? C was the Y intercepts.

So where the line crosses the y-axis, the red line crosses at add five.

So the red line crosses the Y axis when Y is equal to five.

So what about the blue line? Can we do the same thing? Well, what are the gradient of the blue line? The gradient was two.

So this is Y is equal to 2X.

Well, where does that line crosses the y-axis? It crosses the y-axis when Y is two.

That's y equals 2X and two.

And that's the equation of that line.

What about the yellow line? What is the equation of the yellow line? Well, what's the gradient of the yellow line? It's negative one.

So we can write this as Y is equal to negative 1X, and where does it cross the y-axis? At negative one.

So do we have to write that one next to the X? We mathematicians, do we ever write a coefficient of one? No, so this line gets written as Y is equal to negative X, take away one.

That line gets written as negative X, take away one.

So this is how you can tell the equations of lines from the graphs.

You can work out their gradients just by looking at when you go up one on the x-axis, how far up do you go on the Y? You can work out gradients, and we're getting really good at this.

And we can find the Y intercept just by looking where the line crosses the y-axis.

For your independent task, we are going to use that principle to draw straight lines.

So pause the video here and give this a go.

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

Well, let's look at that first line.

Y is equal to 2X at three.

Where does that line cross the y-axis? What is the Y intercept? The Y intercept has a Y ordinate of three.

So it crosses the y-axis when Y is equal to three.

So at that point.

It has a gradient of two, so what does that mean? When the X ordinate increases by one, the Y ordinate increases by two.

So we can work out all the points on this line, using that principle, when the X ordinate increases by one, the Y ordinate increases by two.

And we can use that principle to work out all the points on this line and when you're a joining your lines together, what do you use? You use a ruler, and you join your points together using a straight line.

Now my straight line, what if it won't do that? Cause I didn't use a ruler, but make sure you use a ruler when you draw your straight lines.

What about that second line? That is Y equals negative 2X add one.

Where will that cross the y-axis? Where will that line cross the y-axis? Well, it will cross at.

So when Y is one.

It is a gradient of negative two.

So what does that mean? When the X ordinate increases by one, the Y ordinate it decreases by two.

So there's a point here, and we have a point there, the points there.

So if you look at this, the negative gradient means that your line is tending downwards, when you line is a positive gradient, it tends upwards.

And then for our final line, Y equals X takeaway four.

Where will that cross the y-axis? Good, when the Y ordinate is negative four.

Now is X takeaway four so what's the gradient? One.

So gradient is one, so when the X ordinary increases by one, the Y ordinance increases by one.

So that we'll have points.

And again, when join this with a straight line using a ruler and that's your line, Y equals X takeaway four.

This was Y is equal to 2X at three, and this was Y is equal to negative 2X plus one.

Now, how else could this equation have been written? Well, this equation could have been mentioned as Y is equal to one, take away 2X.

Gets used to seeing both ways, because you will see them written either in this way or this way, when my gradient is negative.

For this explore task, find the equations of each of these lines and lists equations of some linear graphs that would have the same gradient as one of these graphs.

So pause the video here and give this a go.

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

Let's start with the green line.

Well, what's the gradient of the green line? The gradient when you go up one on the x-axes, you go up three on the Y, the gradient is three.

So this is Y is equal to 3X.

Where does it cross the y-axis? When the Y ordinate is two, so it's 3X add two.

All those lines? When you go up one of the x-axis, you go a four on the Y.

So that is, Y is equal to 4X.

Now, if you look at this, you can't see where this line crosses the y-axis.

So how can we figure out where it crosses the y-axis? Well, we can pick a point on the line and see what happens when we multiply the X ordinate by four.

So let's pick this points.

And my point is.

If you do four times four, you get 16.

How'd you get from 16 to eight? Well, what do you do? You take away eight.

So if you were to continue that always nine, you would find it crosses the Y axis at negative eights.

What about the red line? With the gradient of the red line, you go up one on the X, you go up 1/2 on the Y.

The gradient is 1/2 plus Y is equal to 1/2 of X.

And when does it cross? Crosses forces when Y is four.

So add four.

And then what about the purple line? Well, for the purple line, when you go up one on the x-axis, you go down one on the y-axis.

So I need the gradient is negative one.

That's Y is equal to negative X.

Now, where does this cross the y-axis? At six, or negative X at six.

How else can you see this written? Can be written as y is equal to six takeaway X.

So those are the equations of your lines.

Now, you could have an equation, Y is equal to 3X add seven.

That has the same gradient as 3X add two, but it would cross the y-axis where? When the Y ordinate is seven.

Really well done.

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

Thank you for participating in today's lesson.

I will see you again next time.