how to find constant of proportionality

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What is the Constant of Proportionality? | 7th Grade | Mathcation.com

What is the Constant of Proportionality?

The Constant of Proportionality is the relationship between two related variables. In order to explain how to find the Constant of Proportionality you must understand the relationship between the two variables. The variables must be directly related. In other words, they must have a relationship where one variable directly effects the other variable. For the variables to be a proportion, the ratio of the two variables must be constant. If there is a constant that you can can multiply to one variable to get the other variable, then the two variables are a proportion. The constant that you use to multiply by the variable is called the Constant of Proportionality. Divide the two variables and that is how to find the Constant of Proportionality.

Common Core Standard: 7.RP.2

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What is the Constant of Proportionality

Breaking Down the Constant of Proportionality Definition

The Constant of Proportionality is the connection between two related factors. How to find the Constant of Proportionality you should determine the connection between the two factors. The factors must be directly related, in other words they should have a relationship where one variable directly impacts the other variable. For the factors to be proportional, the proportion of the two factors must be consistent. That means that you will be able to divide on factor by the same divisor to get the other factor.

2 Quick Steps to answer any Constant of Proportionality Example Problem

The Constant of Proportionality is the ratio between two variables.
To find the ratio, you divide one variable by the other variable to get the Constant of Proportionality.

Watch the video explanation of our Constant of Proportionality Worksheet

Watch our free video on how to solve Constant of Proportionality. This video shows how to solve problems that are on our free Constant of Proportionality worksheet that you can get by submitting your email above.

Watch the free Constant of Proportionality video on YouTube here: What is the Constant of Proportionality Video

Video Transcript:

This video is about how to find the constant of proportionality. You can get the worksheet used in this video for free by clicking on the link in the description below.

The first part of understanding what is the constant of proportionality is understanding that the constant of proportionality is the ratio between two proportional quantities. This is typically shown using the equation y equals k x or k equals y divided by x. We're going to focus on the second equation which is k equals y divided by x. K in this equation is the constant of proportionality, y represents the y values, and x represents the x values. We're trying to solve for k because k is the constant of proportionality. In order to figure out k, you take the y value from the y columns and you divide it by the x value from the x columns. We know our formula is k equals y divided by x. If we look at our first row in this example table, we see that the first value of y is 8. We're going to put 8 in for the y value and then the first value of x is 1. We put 1 in for the x value. Then when you simplify this you divide 8 divided by 1 and you get 8. We could use the second row to do a second example. If we had k again, we know our formula is k equals y divided by x, the second row our y value is 16. We're going to use 16 divided by our x value which is 2 and then when you simplify 16 divided by 2 you still get 8. Now we know that k is 8 and, it doesn't matter how many rows you use you will always get 8 for k in this example. The constant of proportionality will not change no matter which row that you use. We know that the equation for the constant of proportionality is y equals k times x. We just found out that k was eight so we're going to take this eight and substitute it in for k. Our equation is going to be y equals eight x and that's the solution. The important thing to remember is that the constant of proportionality definition is the ratio between the y values and the x values let's do a couple practice problems on our constant of proportionality worksheet.

Number four on our constant of proportionality worksheet gives us a table with x values and a table with y values. it's asking us to solve for k, which is the constant of proportionality. Now if you remember the constant proportionality definition states that it's the ratio between the y values being divided by the x values. In order to figure out our constant of proportionality we're going to use the equation k equals y divided by x. We're going to take our first y value, in this case is 12. We're going to take 12 and we're going to divide it by our first x value, which in this case is 2. We do 12 divided by 2 and we get 6. We know our constant of proportionality is 6. The equation for a constant of proportionality is y equals k times x we just found out that 6 is k. We'll substitute 6 in for k. Now we have y equals 6 x as our equation and we know that is the solution to this table. Hopefully this video is helpful for helping you answer the question what is the constant of proportionality.