Lesson video

Hello, my name is Mr clasper and today we are going to be looking at other direct proportion relationships.

Not all direct proportion relationships are linear.

Here is an example.

y is directly proportional to x squared given that y is equal to 36.

When x is equal to three, find a formula for y in terms of x, and the value of x when y is equal to 12.

Well, the first thing we need to do is write our equation.

And we know that if y is directly proportional to x, this gives us an equation of y equals kx.

So what do you think, a statement like y is directly proportional to x squared would give us as an equation that will be, y equals kx squared For step two, we can substitute the information given.

So from the question, we know that when y is equal to 36, x must be equal to three.

Therefore 36 must be equal to k multiplied by three squared.

And we know three squared is nine.

So therefore 36 is equal to k multiplied by nine, and K must be four.

So our constant of proportionality is four, giving us an equation of y equals four x squared.

for part B, we need to find the value of x when y is equal to 12.

This would mean that 12 is equal to four x squared and dividing both sides by four, this would mean that three is equal to x squared and therefore x must be equal to the square root of three Here are some questions for you to try.

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

And here we are solutions for question one and two.

So question one, you should start with an equation of y is equal to kx squared.

And be careful when substituting into this.

So make sure you square your value for x.

And for question two, your equation will be p is equal to k root Q.

And again, make sure you're careful when substituting.

Here are some more questions for you to try.

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

Anterior solutions for questions three and four.

So for question three, you need to substitute the values of x is equal to 100, an x is equal to 20 into the equation x is equal to kz squared, you should find the constant of proportionality of 0.

25.

And once you find this formula, you should be able to find the other two missing values by substituting carefully.

And for question 4 just be careful with this one.

We have dimensions in both centimetres, and in metres.

So we need to be careful with this.

I've chosen to move ahead with metres.

So I changed 50 centimetres and converted this to naught.

5 metres.

And likewise with 60 centimetres, I converted this to 0.

6 metres.

When you put this into the equation, you should end up with h is equal to 126.

4d cubed, and substituting 0.

6 into this will give you 27.

3 metres as a final answer.

And that brings us to the end of our lesson.

So we've been looking at different direct proportion relationships.

I want to give the exit quiz ago to show off your new skills.

`I'll awfully See you soon.