## The Constant of Proportionality

#### Aligned To Common Core Standard:

**Grade 7 Proportional Relationships** - 7.RP.A.2b

What is the Constant of Proportionality? In mathematics, we are often faced with constants in several questions. You found them in different alphabets, such as k, c, or any other alphabet. Have you ever wondered what is constant? Well, if you are new to this concept, let us tell you that you should know what a constant and then explore it further because, trust us, it is going to help you a lot is. A constant in mathematics is a number or any alphabet that's given a constant value fixed by definition. An alphabet or symbol denote this constant number. This constant value is used to facilitate the solution of many mathematical problems. Now coming to the famous constant, â€˜the constant of proportionality.' It is the proportion between two directly proportional numbers. These directly proportional numbers have an impact on each other in a way that an increase or decrease in one number marks an increase or decrease in the other quantity too. The constant value is often written as or denoted by k. It is a ratio between values of x and y and written as: K = y/x Putting it another way : y = kx

### Printable Worksheets And Lessons

- Graph Work Step-by-step
Lesson- Find the constant within the line graph.

- Guided Lesson
- You will find three graphs that you need to work with. They mimic
most test questions on this skill that I have seen.

- Guided Lesson
Explanation - I tried to simplify how I answered these questions.
Students seemed to work well with it when I tested it on my guinea
pigs; A.K.A. my 7th grade niece.

- Practice Worksheet
- Graphs take up a lot of space, so this one is spread over 4 pages.

- Matching Worksheet - There are just two questions here. Sorry about that, but I like to keep this to one printable page. Another introduction page for you, I guess.

#### Homework Sheets

We look at various graphs and determine where the constant lies within the slope.

- Homework 1 - The graph of a proportional relationship is a straight line that passes through the origin. Proportional quantities can be described by the equation y = kx, where k is a constant ratio.
- Homework 2 - The graph is a straight line and it passes through the origin. So, the relationship is directly proportional.
- Homework 3 - The graph below represents the number of tables transported and the number of trips made. What is the constant of proportionality?

#### Practice Worksheets

Once you determine the equation used, it's a relatively simple topic.

- Practice 1 - The graph represents the sales at one bookstore.
- Practice 2 - The graph represents the distance (km) covered by a train over time.
- Practice 3 - Look at each graph below and determine the constant of proportionality.

#### Math Skill Quizzes

These are the types of quizzes that you can expect at this level.

**How to Determine the Constant of Proportionality** - A constant of proportionality to some people sounds like something extremely complicated, but there is a strong possibility that you have encountered it at least once before.
Imagine you are in a grocery store on a Saturday morning with your family. You have been asked to pick some tomatoes. When you reach the aisle, you see a sign that says $3.00 for two tomato cans. You immediately divide the amount with two and you realize one tomato can costs $1.50. What you did was finding the constant of proportionality for the tomato can.
The constant of proportionality is the ratio between two quantities that are directly proportional. In the above example, the ration is $3.00/2 which is equal to $1.50. These two quantities are directly proportional, which means that they increase and decrease at an equal rate. The price of the tomato can increase and decreases correspondingly, depending on how much you buy.
A constant of proportionality is a fixed value that remains unchanged and can help determine variable quantities of the same object.