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## What You Need to Know About Proportional Relationships

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Andrew Lee
April 20, 2021

A proportional relationship, sometimes known as the constant of proportionality, relates two quantities according to a common ratio. In other words, the same proportion!

If you are in seventh grade and looking to review common core state standards (CCSS), you will need to be familiar with this term. Not only will you see it in school, but you'll find it has many real-world applications. Let's dive in!

## Proportional Relationships in Algebraic Formulas

A proportional relationship means that two or more things are directly proportional, or that the quantities increase or decrease according to equivalent ratios. We can state this proportional relationship with the formula, y = kx. Y and x here are the quantities that are proportional to each other. The k here is called the constant of proportionality, sometimes known as the unit rate.

We can see this in real-life applications: If the cost of an apple is \$1.50 per pound, as the number of apples you buy (let’s use x) increases, the total cost you will have to pay (let’s use y) goes up at the same rate.

Let's replace the formula above with \$1.50 as our constant of proportionality.  ## Graph of a Proportional Relationship

While you can work with proportional relationships in algebraic form, you can also see it visually by graphing it on a coordinate plane. The graph shows that a proportional relationship is always a straight line through the origin.

If you are used to graphing lines with the formula y = mx + b, you'll see that the graph of a proportional relationship is simply a linear relationship without the b. That means it will always go through the origin (0,0).

Let’s graph our example of buying apples at \$1.50 per pound. The y value represents the total cost, while the x value represents the number of apples that you buy. You can see that for every unit of increase along the x-axis, there are 1.5 units of corresponding increase in the y axis. ## How to Review Proportional Relationships

If you are looking to review proportional relationships and are tired of only completing worksheets, try working through real-life problems. If you are an interactive learner, you will see how often proportional relationships appear in real life. Just look for the constant of proportion k when you remember the formula y = kx.

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