Solve simple kinematics problems (velocity, initial velocity and acceleration formulae)

﻿Hello, my name is Mr. Clasper and today we are going to be looking at simple direct proportion using y is equal to kx. One way to think of direct proportion is as one amount increases, another amount increases at the same rate. Let's take this example. If bananas cost 30p each, how much do two bananas cost? We could calculate two multiplied by 30. This would give us 60p. How much do five bananas cost? We could calculate five multiply by 30 and this would give us one pound 50. How much do 10 bananas cost? We could calculate 10 multiply by 30p and this will give us three pounds. Can you see how the cost is directly proportional to the number of bananas? So when I multiply the number of bananas by 10 for example, I also multiply the price by 10. How much do n bananas cost in pence? Well, we calculate this with n multiplied by 30 and this is equal to 30n. This shows a direct proportion relationship. If we say that y is the cost of a banana, and x is the amount of bananas, we can say that y is proportional to x. Instead of writing y is proportional to x, we often use the symbol in this box. The direct proportion relationship is of the form y is equal to kx. So again in our example, the cost of bananas is equal to a constant, which we call k, multiplied by the number of bananas. We call k the constant of proportionality. Can you see what k is in our banana example? Well, in our example, the value of k or the constant of proportionality would be 30 as this is the number which we multiply each new amount of bananas by. 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 remember, in this example, the cost of a burger, which is three pounds will be our constant of proportionality as every new amount that we have it's going to be multiplied by three. For part d, Ina spends 12 pounds on some burgers, how many does she buy? So we can take this total amount and divide it by our constant which would give us four. And for part e, how much do x burgers cost? We still do the same thing. So we can multiply x by the constant which will be three so therefore we get 3x. Here's another 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 in the table, if one cube is 2.5 centimetres tall, then logically two cubes will be double this, so we get our five and each time we are multiplying the number of cubes by 2.5 as this is our constant of proportionality. So the height of each cube does not change. And for part b, explain why this shows a direct proportion relationship. This is because the constant of proportionality is 2.5. So we can take any number of cubes and multiply this by 2.5 to find the height of the given tower. Y is directly proportional to x, given that y is equal to 10 when x is equal to two, find a formula for y in terms of x and the value of y when x is equal to 20. Our first step is to write down the equation. So we're told that y is directly proportional to x, therefore, y must be equal to kx. I then need to substitute the information, so I've been told that when y is 10, x must be equal to two. And substituting this in, if we know that 10 must be equal to two lots of k, then k must be equal to five. Now, I can make my formula. So my formula is y is equal to 5x. For part b, we need to find the value of y when x is equal to 20. So using this formula, if I know that x is equal to 20, I can substitute it into the formula, and five multiplied by 20 will give me a value of 100 for y. 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 for question three. So remember, you can start this process by finding an equation. So y is equal to kx, and then finding your constant of proportionality, which in this case was five. Once you have this, we can use our equation y is equal to 5x to find the values of y and x in parts b and c respectively. And for part d, as y is directly proportional to x, this means we get a graph which must start from the origin and it must be a straight line. Here's another 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 remember, the first step is to write your equation. So you can write y is equal to kx and if you consider y to be the number of pages in the book and x to be your time, then you can work out your equation. Once you have your equation, substitute your amounts, and everything should work out. And that is the end of our lesson. So we've been using simple direct proportion using the equation y is equal to kx where k is the constant of proportionality. Why not try the exit quiz to show off your new skills. I'll hopefully see you soon.

1. An orange costs 40 pence. How much do 8 oranges cost?

Simple Direct Proportion

In this lesson, we will use the formula y=kx to describe directly proportional relationships.

Maths

Y11 Maths (Higher)

Key Stage 4

Year 11

Simple direct proportion y = kx

Direct and Inverse Proportion

Algebra (A)

THEME

UNIT

Other direct proportion relationships

Inverse proportion

Further proportionality

1. y is directly proportional to x and x is inversely proportional to z². y = 20 when x = 5 and z = 2 when x = 3 Find a formula for y in terms of x.

2. y is directly proportional to x and x is inversely proportional to z². y = 20 when x = 5 and z = 2 when x = 3 Find a formula for x in terms of z²

3. y is directly proportional to x and x is inversely proportional to z². y = 20 when x = 5 and z = 2 when x = 3 Find the value of y when z = 4

1. y is inversely proportional to 𝑥. Given that y = 2 when 𝑥 = 3, find a formula for y in terms of 𝑥.

2. y is inversely proportional to 𝑥. Given that y = 2 when 𝑥 = 3, what is the value of y when 𝑥 = 4?

3. y is inversely proportional to 𝑥. Given that y = 2 when 𝑥 = 3, what is the value of 𝑥 when y = 12?

4. y is inversely proportional to 𝑥². Given that y = 9 when 𝑥 = 2, what is the value of y when 𝑥 = 6?

Lesson overview:Simple direct proportion y = kx

Core Content

Direct and Inverse Proportion: