Lesson video

Hello, my name is Mr. Clasper and today we are going to be using gradient to solve problems with parallel lines.

The two lines of y is equal to two x plus one and y is equal to two x minus two are drawn on the grid.

What do you notice? The two lines are parallel.

They are travelling in the same direction.

Why is this? This is because both lines have the same gradient.

So both lines are one unit across and two units up.

So when two or more lines have the same gradient, we know that they are parallel.

Write down the equation of the line parallel to y equals four x minus three that passes through the point zero, negative 11.

Well, if I look at my equation, I can see that I have a gradient of four.

And as the other line is parallel, this means my other line must also have a gradient of four.

So my equation must be y is equal to four x plus c.

And we don't know the value of c yet.

If we look at the coordinate given, however, as this is zero, negative 11, c must be equal to negative 11, as this will be our y intercept.

Therefore the equation of this line would be y equals four x minus 11.

Let's take a look at this example.

Write down the equation of the line parallel to x plus two y is equal to 12 that passes through the point zero, 31.

Well, first of all, if I look at this equation, I need to rearrange this into the form of y equals mx plus c so that I can find out my gradient.

So if we subtract x from both sides, we would have two y is equal to negative x plus 12.

I'd also need to divide both sides of this equation by two to make y the subject.

So that means my equation is y is equal to negative one over two x plus six.

And I know that this line has a gradient of negative one over two.

This means my new line has the same gradient.

And if I look at the coordinate given, my y intercept is 31, as it crosses at the point zero, 31.

Therefore my equation is y is equal to negative one over two x plus 31.

Here are some questions for you to try.

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

And here are your solutions.

So if we look at question one, write down the equation of a line parallel to y is equal to two x minus three, as long as you have a line which has a gradient of two, then your answer is correct.

So two examples given were y equals two x plus three or y equals two x minus 10.

So again, if your equation has two x and a constant equal to y, then you have the correct answer.

If we look at part two, we need an equation which is parallel to y equals six x plus one, which passes through zero, eight.

This means we must have a gradient of six and a constant of eight as it passes through zero, eight, or intercepts the y-axis at zero, eight, so your equation was y equals six x plus eight.

And for the last one, we need to rearrange this equation first.

So this means that the given equation has a gradient of negative 0.

5, which means that our new line would also have this gradient.

And as we know it passes through zero, five, we know that the value of c would be five.

And here is your last question.

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

And here is the solution.

So looking at line A, we can see that we have a gradient of two and if we rearrange the equation for line D, we can see that this equation also has a gradient of two, therefore the final answer were lines A and D.

And that brings us to the end of the lesson.

So by now you should be able to use gradient to solve problems with parallel lines.

Let's give the Exit Quiz a go and show off our brand new skills.

I'll hopefully see you soon.