Answering what is a Proportional Relationship?

Get the free Constant of Proportionality from Tables Worksheet and other resources for teaching & understanding how to solve Proportions

How to solve Proportional Relationships

Proportions are statements of equality between two different ratios. All proportions have a multiple that is used to relate one variable to the other variable. The multiple that is used to multiply or divide to get from one variable to the other is called the Constant of Proportionality. Constant of Proportionality is written in the form y=kx, where k is the Constant of Proportionality. You can solve proportions by turning each ratio into a fraction, setting the fractions equal to each other, and then solving for the missing variable.

Common Core Standard: 7.RP.2

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The Equation for Proportional Relationships

What is proportional anyway? In order to find the equation for Proportional Relationships you must understand that a proportion is a ratio between two variables. The equation for proportional relationships is equal to the y variable divided by the x variable. Ok then what’s a proportional relationship? Proportions are explanations of uniformity between two distinct variables. In order to solve proportions you must change the proportions to fractions and then cross multiply to find any missing variables.

3 Short Steps for solving any Proportional Relationship Example

Change each ratio into a fraction.
Set the fractions equal to each other.
Cross multiply to find the missing variable and after determining is it proportional.

Proportional Relationships Practice Problems Quiz

Watch the video explanation of our Proportional Relationships Worksheet

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

Watch the free Constant of Proportionality from Tables video on YouTube here: Proportional Relationships Video

Video Transcript:

This video is about answering the question what is a proportional relationship. You can get the proportional tables worksheet used in this video for free by clicking on the link in the description below. A proportional relationship is a relationship between two variables where their ratios are equivalent. Another way to think about this is that one variable is always a constant value times or divided by the other variable. This constant value is called the constant of proportionality. The constant of proportionality is always represented by the variable k. In order to determine if two values are proportional you have to see if you can multiply by the same constant in order to go from one value to the other. You could also use division to see if you get the same constant. If the constant is equal for all the values then it is proportional. We could use multiplication or we could use division to determine if this relationship is proportional. For the first two I’m going to use multiplication and the last two I’m going to use division. In order to go from our x column to our y column, to go from 2 to 20 we would multiply times 10. 2 times 10 is 20. For the next value do the same thing 8 times 10 is also 80. We’re going from 8 to 80 by multiplying by 10 and 2 to 20 by multiplying by 10 as well. You could use the same process but in reverse if you want to use division instead. To go from y to x 60 to 6 we would divide by 10 and then 70 to 7 we would also divide by 10. This is proportional because the constant in between the values is equal because we are either multiplying by 10 or dividing by 10. The constant of proportionality is 10. Let’s do a couple practice problems on our proportional relationships worksheet pdf.

Looking at number one on our proportional relationships 7th grade worksheet, it gives us a table with x and y values. It asks us if it’s proportional and then if it is proportional it wants to know the constant of proportionality for our proportional relationship equation. In order to determine if this is proportional we have to figure out if we are multiplying by the same amount to go from the x column to the y column, to go from 2 to 4 we’re going to multiply 2 times 2 is 4. To go from 1 to 2 we’re going to multiply 1 times 2 is 2. To go from 7 to 14 again it’s times 2 and then to go from 5 to 10 again we’re multiplying times 2. Because we are using the same constant oF proportionality of multiplying times two we know that this is proportional our constant of proportionality is going to be two.

Jumping down to the second problem on our proportional relationships worksheet. Again, we have to figure out what the constant of proportionality is and then use it to write our proportion relationships equation. in order to go from x to y in our first row 9 to 0 we have to multiply 9 times 0 is zero, to go from three to six we do three times two to get six, to go from two to ten we do two times five to get ten, and then six to three we do six times one half, six times one half is three. Is this proportional the answer is no and I know it’s not proportional because all of our multiplication gives us a different constant to multiply by if they were proportional all of these would be equal.

The last one we’re going to complete on our proportion relationships worksheet is number three. Again this gives us the same setup of a table it asks if it’s proportional and then if it is proportional wants us to complete the proportional relationships equation. To go from 5 to 15 we can multiply time 3. To go from 1 to 3 we multiply times 3 again, to go from 4 to 12 we multiply times 3 again, and then finally you go from three to nine we multiply times three. This is proportional and the constant of proportionality for our equation is three. K equals three. Download and try all of the proportional relationship example problems from our proportional relationship worksheets above.