Lesson video

Hello, my name is Mr. Clasper and today we are going to be finding the gradient of a line.

What is the gradient of a line? Well, the gradient of a line is how steep a line is.

It's how far up or down it goes for every one it goes across.

Let's have a look at some examples.

Let's take this line.

For every one unit across, we move one unit up.

This means that our line has a gradient of one.

Our next line is slightly different.

We can see, by comparing the two, that it is steeper.

For every one unit across, we move two units up.

This means that this line has a gradient of two.

If I look at my next line, this line moves one unit across and one unit down.

This means we have a gradient of negative one.

Our next line, if we move one unit across, we move 1/2 a unit up, or another way to think of this is for every two we move across, we move up one.

This gives us a gradient of 1/2.

And our last example, we move three units across and one unit down, or one unit across and 1/3 of a unit down.

This means we have a gradient of negative 1/3.

Here is a question for you to try.

Pause the video to complete your task and click Resume once you're finished.

And here are your solutions.

So just watch out for a few of these, so for E, for every four units across, we go two units up.

This means for every two units across, we go one unit up, which would give us a gradient of 1/2.

And likewise for F, for every three units across, we go up one unit.

So this means we have a gradient of one over three.

Here is a question for you to try.

Pause the video to complete your task and click resume once you're finished.

And here is your solution.

So for a gradient of three we have one unit across and three units up.

And for a gradient of negative three, we have one unit across and three units down.

From the image given, an added question was what is the same and what is different? So you could say that the lines are reflections of one another, that could be a similarity.

And what is different? The lines are not the same gradient.

How can we find the gradient of this line? Well, from this point we can see for every one unit we move across, we move up three units.

This means we have a gradient of three.

Let's have a look at this example.

For every two units we move across, we move down negative one.

Because we've moved down, this means we have a gradient of negative one over two, or negative 0.

5.

Here are some questions for you to try.

Pause the video to complete your task and click Resume once you're finished.

And here are your solutions.

So for the first image we have a gradient of two, so the line is one unit across and two units up.

And for the second image, this is one unit across and two units down, which gives it a gradient of negative two.

Let's have a look at this question.

Work out the gradient of the straight line which passes through the points, negative two, three and zero, one.

Well, if we were to plot this on a graph, we can plot two points and create our straight line.

Now that we have our straight line, we should be able to find our gradient.

So for every one unit we move across, we move down one unit.

This means we have a gradient of negative one.

Let's have a look at this example.

We've been given the coordinates, negative 12, negative 15 and one, 21.

This might require a slightly different approach.

Let's sketch the graph instead of plotting it.

So we're estimating where the points negative 12, negative 15 go and where the points one and 24 go.

I've joined these with a line segment.

And other pieces of information I can find are the distances between my x coordinates and my y coordinates.

So the difference between negative 12 and one is 13.

And the difference between 24 and negative 15 is 39.

What this means is for every 13 units across, we move 39 units up.

And if we simplify this, we would get a gradient of three, as 39 divided by 13 would give us three.

Here are your last two questions.

Pause the video to complete your task and click Resume once you're finished.

And here are your solutions.

So for the first example you needed to find a difference in y and divide this by your difference in x.

So dividing 18 by six would give you a gradient of three for this question.

And for part B, similar to the last one, we find a difference in y divided by a difference in x.

So if you calculate 18 divided by four, you should get a gradient of 4.

5.

You could also have 18 over four, or nine over two and this would also be correct.

And that brings us to the end of our lesson.

So we've been learning how to find the gradient of a line.

Have a go at the Exit Quiz to show off your new skills.

I'll hopefully see you soon.