This word “relationship” means that we are looking at how two different quantities are connected with each other. Today we will tell you about what is Proportional Relationship.

For example, how is the price of an article related to its amount? Generally (when there is no special offer), the price of an item is proportional to its amount. So, we will see how this type of relation is described mathematically.

When the ratio of one quantity to another is the same in all cases, we say that both quantities are proportional. We can also say that the relation between two quantities is a proportional relation.

**Proportional Relationship.**

If all the ratios of the variables are equal, then the two variables have a proportional relationship.

In other words, in proportional relations, one variable is always a constant value of the other variable. That constant value is called constant of proportionality.

All proportional relations can be represented by an equation: U=kx, where k is the constant of proportionality. Such continuous of proportionality is also called the unit rate.

**Graph of A Proportional Relation.**

While you can work in algebraic form with proportional relations, you can also see it graphically on a coordinate plane. The graph shows that a proportional relation is always a straight line through the origin.

If you are accustomed to graphing lines with the formula y = mx + b, you will see that the proportional relation has only one linear relation without the graph b. This means that it will always pass through the original (0,0).

**Video Source:** Proportional vs. Non-Proportional (Relationships on Graphs)

**How To Review Proportional Relationships.**

If you want to review proportional relationships and are tired of just completing worksheets, try working through real-life problems.

If you are an interactive learner, you will find how often proportional relationships appear in real life situations. When you recall the formula of y = kx just look at the constant of the ratio k.

**Example.**

“Yesterday, I put 10 gallons of gas in my jeep and paid $30. A few hours later, I went back to the gas station with my father’s car and after filling the tank, paid $18. How many gallons of gas I had put in my dad’s car?”

To solve this problem, first we have to find the proportionality ratio between the gallon I put in our car and the amount I paid.

$30 ÷ 10 gallons = $3/gallon ($per gallon)

After that, once we know that the ratio is $3/gallon, we need to calculate how many gallons we can put with $18 in the tank.

$18 ÷ $3/gallon = 6 gallons

Then again, when I went to the gas station for the second time, I filled 6 gallons of gas in my dad’s car.

This situation illustrates a clear example of proportional relations where the amount of the first fill is proportional to the amount of the second fill. The quotient obtained by dividing the two is the same in both the cases. This is the ratio.

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